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5

The Distribution System Operator in a d-‐MPC application for USEF

Wouter Kramer EES-‐2015-‐244 Master Programme Energy and Environmental Sciences, University of Groningen

Research report of Wouter Kramer Report: EES-‐2015-‐244 Supervised by: Prof. dr. ir. J.M.A. (Jacquelien) Scherpen, Engineering and Technology Institute Groningen (ENTEG) Prof. dr. H.A.J. (Harro) Meijer, Energy and Sustainability Research Institute Groningen (ESRIG) dr. G.K.H. (Gunn) Larsen, DNV-‐GL D.B. (Bao) Nguyen, Discrete Technology & Production Automation (DTPA) University of Groningen Energy and Sustainability Research Institute Groningen, ESRIG Nijenborgh 4 9747 AG Groningen T: 050 -‐ 363 4760 W: www.rug.nl/fwn/research/esrig

ACKNOWLEDGMENTS

Foremost I would like to express my sincere gratitude to my first supervisor prof. dr. ir. J.M.A.Scherpen for supervising me for 2 Master’s theses in succession and to bring me in contact withDNV GL. It is at DNV GL where the research for this thesis was conducted. Consequently, I wouldlike to thank dr. G.K.H. Larsen for her supervision at DNV GL, especially in guiding me in ModelPredictive Control and the countless hours we spent on solving the mathematical problems along theway. Moreover, her thorough feedback sessions on the research in general and the report in specifichave been much appreciated. I would like to give special thanks to D.B. Nguyen, PhD student atthe University of Groningen I worked with. The discussions on Model Predictive Control were alwaysenlightening and useful. I would like to extend my sincere thanks to him for his contribution as spellchecker. I am looking forward working with him in the next few months in order to use results fromthis thesis for the purpose of an academic paper. I express my gratitude to prof. dr. H.A.J. Meijerfor him being willing to act as my second supervisor on short notice.

The finalisation of this research characterises the end of being a student at the University of Gronin-gen. I am very grateful for all the friends I have made during that time in Groningen.

Wouter Kramer

GroningenAugust 31, 2015

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SUMMARY

Electricity is the fastest-growing final form of energy worldwide and renewable electricity generationis growing rapidly in the global energy mix in the upcoming years. These trends are fuelled byincreasing environmental awareness, especially characterised by a focus on climate change and fossilfuel use and embodied by legislation (e.g. the Europe 2020 growth strategy). Renewable energysources are characterised by their intermittency and a large share of this renewable energy will beproduced decentralised. It is therefore evident that the current, centralised, energy systems are facingmajor challenges with respect to design and maintenance. A transition from the current centralised,or top-down, energy grid to a fully bidirectional grid is at hand. This future grid is often referred toas a smart grid. The Universal Smart Energy Framework (USEF) will enable the transition towardsa modern and smart energy system that is safe, reliable, affordable and will become increasinglysustainable.

Load shifting, energy storage and management of local generation in the distribution grid providenew means to unleash flexibility, qualitatively defined as the shift ability of loads in time. WithinUSEF, this flexibility can be accessed for peak load reduction and active balancing. A central aspectwithin USEF is the Market-based Control Mechanism (MCM) relating to active balancing. Thismechanism allows the continuous optimisation between supply and demand of energy. Algorithmsare necessary within the MCM. It was previously demonstrated that distributed Model PredictiveControl (d-MPC) can be applied to the green and yellow regime of the operation phase of the MCMwithin USEF in order to balance power in a network of prosumers.

The current d-MPC applications exclude the role of the Distribution System Operator (DSO) whosegoal is to minimise grid capacity costs while simultaneously safeguarding security of supply. Thisgives rise to the aim of this research; to investigate and embed the role of the DSO within the givend-MPC application to control the MCM, the central component of USEF. In the setting of USEF,the DSO can procure flexibility if the physical limits of the distribution grid are reached in order toease the load and prevent damage to assets.

The resulting application acts as an internal optimisation tool for the aggregator, accumulating theflexibility of prosumers, in order to find an optimal sequence of turning flexible devices on and offthat minimises the imbalance between electricity supply and demand. Simultaneously it must ensurethat this optimal sequence does not violate capacity constraints on the transformer connecting theprosumers in the low voltage distribution grid. Congestion, the overloading of the transformeris prevented by means of a market mechanism and the addition of a Lagrange multiplier and anassociated sub-gradient method to the application. The fit of this application with USEF is in detailelaborated upon.

A MATLAB model is build in which the application is simulated and analysed. By shifting the flexibleload of the heat pump of prosumers in time, imbalance is minimised and congestion is prevented.It is concluded that congestion can only be detected and thus be prevented within the predictionhorizon of the d-MPC application. Moreover, preventing congestion results in worse performancewith respect to minimising the overall imbalance since congestion management alters the optimalsequence that minimises the overall imbalance in the network of prosumers.

Several assumptions and simplifications with respect to the complex MCM of USEF are made dueto either limitations of the given applications or due to the applied focus on the DSO within thisthesis. The presented d-MPC application only considers a single BRP, a single aggregator and asmall amount of prosumers connected to a single transformer. Future topics of interest includeupscaling the number of actors, increasing the number of capacity constraints within the networkof prosumers, considering micro CHPs next to heat pumps and the notion of real prices next toeconomic signals (the Lagrange multipliers) in order to assess the value of flexibility in the envisionedsmart grid.

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SAMENVATTING

Elektriciteit is wereldwijd de snelst groeiende vorm van energie en duurzame elektriciteitsproductieis snel groeiende in de energie mix. Deze trends worden gevoed door een toenemende mate van mi-lieubewustzijn en worden verankerd in wetgeving (bijvoorbeeld de Europa 2020-strategie). Duurzameenergiebronnen worden gekenmerkt door de variabiliteit en een groot deel van de duurzame energie zaldecentraal worden geproduceerd. Het is daarom evident dat de huidige, gecentraliseerde, energie sys-temen met grote uitdagingen met betrekking tot het ontwerp en onderhoud worden geconfronteerd.Een transitie van het huidige gecentraliseerde, top-down, energienet naar een volledig tweerichtingennet is aanstaande. Een dergelijk toekomstig net wordt vaak aangeduid als een smart grid. HetUniversal Smart Energy Framework (USEF) zal de transitie naar een modern en slim energie systeemwelke zowel veilig, betrouwbaar, betaalbaar is en immer duurzamer zal worden mogelijk maken.

Het verschuiven van belastingen in de tijd, energie opslag en het bestuur van lokale productie inhet distributienet bieden nieuwe mogelijkheden om flexibiliteit te winnen. Deze flexibiliteit kan bin-nen USEF worden gebruikt om piekbelasting te reduceren en om actief te balanceren. Een centraalaspect binnen USEF is het Market-based Control Mechanism (MCM) welke relateert tot het actiefbalanceren. Dit mechaniek stelt in staat om continu vraag en aanbod van energie te optimalis-eren. Algoritmen zijn binnen MCM benodigd. De toepasbaarheid van distributed Model PredictiveControl (d-MPC) in het groene en gele regime van de operate phase van MCM binnen USEF isin voorgaand werk, waarin het vermogen in een netwerk van prosumers kan worden gebalanceerd,gedemonstreerd.

De huidige d-MPC applicaties negeren de rol van de Distribution System Operator (DSO) welke hetminimaliseren van de kosten van netcapaciteit en tegelijkertijd het waarborgen van leveringszekerheidals doel kent. Dit leidt tot het doel van dit onderzoek; het onderzoeken en toevoegen van de rol vande DSO binnen de bestaande d-MPC applicatie om de MCM, het centrale component van USEF aante sturen. In de context van USEF kan de DSO flexibiliteit opkopen wanneer de fysieke limieten vanhet distributienet bereikt worden om schade aan infrastructuur te voorkomen.

De applicatie dienst als interne optimalisatie tool voor de aggregator, die de flexibiliteit van deprosumers samenvoegt, om een optimale volgorde van het aan- en uitschakelen van flexible apparatente vinden welke de onbalans tussen vraag en aanbod minimaliseert. Tegelijkertijd moet de aggregatorwaarborgen dat deze volgorde de capaciteitslimiet van de transformator, die de prosumers verbind,niet schendt. Congestie, de overbelasting van de transformator wordt voorkomen door middel van eenmarktmechanisme en de toevoeging van een Lagrange-multiplicator en een bijbehorende subgradientmethode aan de applicatie. De relatie tot USEF is op detailniveau beschreven.

Een MATLAB model is gemaakt om de applicatie te simuleren en te analyseren. Door het verschuivenvan de flexible belasting van warmte pompen van prosumers wordt de onbalans geminimaliseerd encongestie voorkomen. Congestie kan enkel in de voorspelling horizon van de d-MPC applicatieworden gedetecteerd en worden voorkomen. Het voorkomen van congestie leidt tot een verminderdresultaat met betrekking tot het minimaliseren van de onbalans. Dit vanwege het feit dat de optimalevolgorde welke de onbalans minimaliseert in een netwerk van prosumers zal moeten worden gewijzigdom congestie te voorkomen.

Meerdere veronderstellingen en vereenvoudigingen zijn gemaakt ten aanzien van het complexe MCMvanwege de beperkingen van de huidige d-MPC applicaties en de nadruk op de DSO in dit onderzoek.De gepresenteerde d-MPC applicatie beschouwt een enkele BRP, een enkele aggregator en een kleinnetwerk van prosumers die verbonden zijn met een enkele transformator. Interessante thema’s voorverder onderzoek zijn het opschalen van de aantallen partijen, het in beschouwing nemen van warmte-krachtkoppeling, het verhogen van het aantal capaciteitslimieten en de toevoeging van echte prijzen integenstelling tot de economische signalen (de Lagrange multiplicatoren) om de waarde van flexibiliteitin de beoogde smart grid te kunnen bepalen.

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TABLE OF CONTENTS

1 INTRODUCTION 131.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.2 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2.1 Research Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2.2 Research Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.1 Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 UNIVERSAL SMART ENERGY FRAMEWORK 172.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 USEF actors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Market-based Control Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Changing role for the Distribution System Operator . . . . . . . . . . . . . . . . . . 222.5 Distributed Model Predictive Control in USEF . . . . . . . . . . . . . . . . . . . . . 24

3 FLEXIBILITY 273.1 Types of flexibilty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Quantification of flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Ramp up flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Ramp down flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 MODEL PREDICTIVE CONTROL IN SMART GRIDS 334.1 Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Distributed Model Predictive Control as Market-based Control Mechanism . . . . . . 34

4.2.1 Coupling of prosumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2.2 Day Ahead Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 USEF interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 DISTRIBUTED MODEL PREDICTIVE CONTROL INCLUDING THE DSO 435.1 Congestion management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 Congestion management via Lagrange multipliers . . . . . . . . . . . . . . . . . . . 435.3 Day Ahead Planning and goal function . . . . . . . . . . . . . . . . . . . . . . . . . 475.4 USEF interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 SIMULATION SETUP 536.1 Network coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.2 Flexible appliances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.3 Capacity constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.4 Excessive state switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.5 Demand patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.6 Performance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7 SCENARIOS 617.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

8 SIMULATIONS 638.1 Quantification of flexibility to divide the Day Ahead Planning . . . . . . . . . . . . . 638.2 Congestion Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8.2.1 Simulation 1, 3 prosumers on a 12 hour time horizon . . . . . . . . . . . . . 668.2.2 Simulation 2, 3 prosumers on a 24 hour time horizon . . . . . . . . . . . . . 72

8.2.3 Simulation 3. Adjusted Day Ahead Planning. . . . . . . . . . . . . . . . . . 748.2.4 Simulation 4, 3 prosumers on a 24 hour time horizon. Relaxed constraint. . . 76

9 CONCLUSION 799.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

REFERENCES 83

ACRONYMS

The following acronyms are used throughout this thesis.

• ADS Active Demand and Supply• BRP Balance Responsible Party• DAP Day Ahead Planning• DER Distributed Energy Resource• d-MPC Distributed Model Predictive Control• DNO Distribution Network Operator• DR Demand Response• DSM Demand Size Management• DSO Distribution System Operator• ESCo Energy Service Company• MIQP Mixed Integer Quadratic Programming• MCM Market-based Control Mechanism• MPC Model Predictive Control• TSO Transmission System Operator• USEF Universal Smart Energy Framework• µ-CHP Micro Combined Heat and Power

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1 INTRODUCTION

1.1 Motivation

With respect to global energy markets, two major trends are observed by the International EnergyAgency. Firstly, electricity is the fastest-growing final form of energy worldwide and will remain sowith a projected annual growth of 2.1% up to 2040, according to the New Policies Scenario of theWorld Energy Outlook 2014 (IEA, 2014b). Secondly, renewable electricity generation is growingrapidly in the global energy mix from 17% in 2007 to 22% in 2013 and a projected share of 33%in 2040 (IEA, 2014a). These trends are fuelled by increasing environmental awareness, especiallycharacterised by a focus on climate change and fossil fuel use (Ecorys and ECN, 2014) and embodiedby legislation (e.g. the Europe 2020 growth strategy). The goals set by the Netherlands for 2020include a 16% CO2 emission reduction compared to 1990 and a share of 14% renewable energyproduction (Rijksoverheid, 2015). Renewable energy sources are characterised by their intermittencyand a large share of this renewable energy will be produced decentralised. It is therefore evidentthat the current, centralised, energy systems are facing major challenges with respect to designand maintenance (Scherpen, 2015). One example of such a challenge is system security of anelectricity network with more and more dispersed energy generation. The solar eclipse of March 20,2015 resulted in a drop of 35 GW in solar PV production in Europe over a period of less than 2hours. As the European network is the world’s largest interconnected grid, managing this event wasan unprecedented challenge (European Network of Transmission System Operators for Electricity,2015).

A transition from the current centralised, or top-down, energy distribution grid to a fully bidirectionalgrid is at hand. In this envisioned grid, end users are described as prosumers, actors that both produceand consume electricity. Moreover, this future grid is often referred to as a smart grid that is capableof intelligent monitoring, control and communication (DNV-GL, 2015). It enables a shift fromproducing energy according to demand to demand energy according to production (Halvgaard, 2014).This allows for introducing fluctuating decentralised energy production into the grid. Combined withthe fact that the electricity network has little storage capability, as opposed to the gas network forexample where gas is stored naturally, controlling the demand side of the prosumer has to ensurean economically efficient, sustainable power system characterised by low losses, high quality, securityof supply and safety (Ecorys and ECN, 2014). The Universal Smart Energy Framework (USEF) willenable the transition towards a modern and smart energy system that is safe, reliable, affordable andwill become increasingly sustainable (USEF Foundation, 2014).

The USEF Foundation (2014) defines the concept of USEF and its components. USEF provides anon-discriminatory access to smart energy systems for all active stakeholders at acceptable costs-to-connect and cost-to-serve levels. The framework provides a set of specifications, designs andimplementation guidelines enabling a fully functional smart, fully bidirectional, energy system. Loadshifting, energy storage and management of local generation in the distribution grid provide newmeans to unleash flexibility (i.e. the shift ability of loads in time). Within USEF, this flexibility canbe accessed for peak load reduction and active balancing. Reducing the peak load by utilising theprovided flexibility results in deferring or avoiding grid reinforcements that were otherwise requiredgiven a peak increase due to the electrification of the economy. A central aspect within USEF is theMarket-based Control Mechanism (MCM) relating to active balancing. This mechanism allows thecontinuous optimisation between supply and demand of energy from all assets and seeks the mosteconomic dispatch pattern and the lowest costs for the overall system. Costs are saved by reducinggeneration and imbalance costs. Generation cost are reduced by shaping the load profile which resultsin less use of peak generation capacity. Consequently, the peak generation capacity can be reduced.Furthermore, imbalance costs (i.e. the costs associated with the imbalance between electricity supplyand demand) such as load curtailment are prevented by enhanced system flexibility.

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Algorithms are necessary within the MCM. An optimal control problem entails the minimisation of acost function proves to be solvable by Model Predictive Control (MPC) (Larsen, 2014) (Pons, 2013).The cost function relates to the aim of the MCM as described before; seeking the most economicdispatch pattern and the lowest cost for the overall system. Larsen (2014) showed in her dissertationthat distributed MPC (d-MPC) is suitable to apply within smart grids due to scalability and theability to anticipate future situations in the network. The notion of a distributed MPC relates to thedecomposition of a central problem. In such a central problem, the goal to minimise the overall powerimbalance in a network of prosumers requires that one central controller knows all the information ofprosumers in that network (Larsen et al., 2012). Due to the competitive nature of the energy market,such information sharing is highly unlikely (Biegel et al., 2012b). Therefore, distributed control ispreferable. Another important reason for distributed control is that decomposition eases computingtime. Centralised MPC is characterised by an overwhelming amount of decision variables, whereas ina distributed MPC the central problem is divided into many smaller optimisation problems that can besolved locally (Giselsson and Rantzer, 2010). Decomposition methods for solving large-scale controlproblems ensure that local actors that might have competing objectives and different constraints cansolve their own optimisation problem, but within a larger framework ensuring, for example, overallgrid stability (Halvgaard, 2014).

Pons (2013) demonstrates a specific application of d-MPC within USEFs MCM operate phase inorder to balance power in a network of prosumers. A design is made in which coupled prosumersare optimised in order to reduce imbalance. A reduction in imbalance relates to cost savings and anoptimal sequence of turning flexible appliances on and off ensures a minimisation of costs. The modelof Pons shows some simplifications. Although Pons described the d-MPC applicable within USEF,due to time constraints only a centralised MPC has been coded and simulated. Extending the workof Pons, Doddema (2014) focuses on the scalability of the specific d-MPC application by coding thedistributed algorithm. By doing so, simulations can handle 100.000 prosumers, whereas simulationsin the work of Pons only consider 30 households. Doddema (2014) shows that in the distributedalgorithm the computation time scales approximately linear with the number of prosumers whereasin the centralised algorithm the relation between computation time and the number of prosumers isgreater than exponential.

In both models, the role of the Distribution System Operator (DSO) as grid operator is not included.It is the grid operator’s goal to minimise grid capacity costs while simultaneously safeguarding securityof supply. Due to the liberalisation of the European power market, congestion management shouldbe handled via markets rather than by regulations (Biegel et al., 2012b). In the setting of USEF, theDSO can procure flexibility if the physical limits of the distribution grid are reached in order to easethe load and prevent damage. The transition towards a bidirectional energy grid and the quest for asafe and reliable system thus asks for incorporating the role of the DSO and grid constraints in thecurrent d-MPC application of Doddema (2014) to better fit with USEF’s MCM.

1.2 Research Objective

1.2.1 Research Aim

Pons (2013) argues that his model is not designed to handle two parties, both the BRP and the DSO,who are both procuring flexibility. The problem of an incomplete model is regarded as a scientificproblem. The model is incomplete and there is a lack of understanding on how the DSO should beembedded and how the model would perform with the introduction of the DSO.

The aim of this research is to investigate and embed the role of the DSO within the given d-MPCapplication to control the MCM, the central component of USEF. The current application lacks amechanism able to handle flexibility requests of the DSO in order to avoid congestion. This research

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can thus be classified as fundamental research in order to expand the current d-MPC application andunderstand the role of the DSO as described by USEF in the setting of this specific application.

1.2.2 Research Question

The following research question is derived in order to reach the desired aim as described above.

• How can the role of the DSO be embedded in the given d-MPC application in USEF’s MCM?

This is an prescriptive research question to identify how the DSO should be embedded in the d-MPCapplication. To answer this research question and steer the research, the following sub-questions aredefined:

1. How can the role of the DSO best be translated in order to be applicable to the d-MPCapplication compliant with USEF?

The first part of the research encompasses the search for ways to incorporate the DSO into themodel. The constraints of the grid will be explored. These constraints have to be related tocosts in order to include them in the costs functions that are minimised in the d-MPC applica-tion. Moreover, the embedding should logically fit within USEF. Therefore, an understandingof USEF is required.

2. How can the current d-MPC application be extended?

The second part of the research is the actual coding of the intended expansion. The mostup-to-date model of the d-MPC application will act as the basis upon which the expansion willbe built.

3. How does the d-MPC application perform?

The introduction of the DSO to the application will have an effect on the optimal sequence.The extent of the effect is of interest. Moreover, a comparison can be made with the resultsof the application without the embedding of the DSO.

1.3 Research Methodology

A modelling study methodology is adopted in order the answer the prescriptive research question.As stated before, the work of Larsen (2014) and Doddema (2014) prove the concept of successfullyapplying d-MPC in smart grids in general and in the operate phase of USEFs MCM in specific.Therefore it can act as a starting point for this research. Thereafter, the specific role of DSO withinthe new system has to be investigated through literature which encompasses USEF description.Consequently, that role has to be specified in such a fashion that it can be added to the existingmodel. It is believed that the addition of the DSO acts as an additional constraint on the model.Whereas in the current model, prosumers can solve their own local optimisation problem given a setof local constraints, the addition of a grid constraint will couple the prosumers, since their combinedload on the network determines the presence and magnitude of congestion. The embedding ofthis constraint asks for a different approach than, for example, a local constraint on an specificprosumer.

The mathematical model is implemented in a MATLAB model. MATLAB allows for easy modifica-tions and additions and provides a simulation environment in which the model can be tested. TheMATLAB model will act as an ordering tool to describe, analyse, simplify and understand the optimalcontrol algorithm within the complex MCM in a USEF compliant energy system.

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1.3.1 Boundaries

The given d-MPC application of Doddema (2014) acts as a starting point. Therefore, the boundariesapplying on that model apply to this work as well. That model solely fits within the operation phaseof USEF. In Chapter 2, USEF in general and the different phases in specific will extensively elaboratedupon. Moreover, the current modelling only considers flexible appliances that produce heat, and incombination with a heat storage tank, yield flexibility that can be altered to minimise a cost function.In specific, the MPC algorithm by Pons (2013) considers heat pumps and µ-CHPs which consumeand produce electricity respectively in producing heat to the heat buffer. Doddema (2014) solelytakes heat pumps in to account in his d-MPC algorithm. Due to the focus on the DSO, this researchsolely addresses heat pumps as flexible device when extending on the actual d-MPC algorithm inMATLAB.

1.4 Thesis Outline

This thesis is structured as follows. In Chapter 2, the Universal Smart Energy Framework is indetail elaborated upon. This includes the actors, their changing roles and the different operatingregimes within the smart grid as envisioned by USEF. Moreover, the MCM will be explained andthe specific role of the DSO within the USEF framework will be analysed. Chapter 3 involves thenotion of flexibility. This entails a definition of flexibility and the quantification of flexibility that canbe provided by a heat pump which will be used later on in Chapter 5 to appoint specific goals toindividual prosumers. Chapter 4 introduces the notation of the MPC and the d-MPC for the problemat hand. In Section 4.3 in specific, the fit of the given d-MPC application with the MCM of USEF isexplained to highlight which of the characteristics of the MCM are included and which are excludedin the application. In Chapter 5, the actual extension, the embedment of the DSO, is mathematicallydefined. In Section 5.4, the fit of the extended application with the MCM of USEF is explained.By extending the d-MPC application with the role of the DSO, the application should better fitwith the complex MCM. In order to run simulations, a MATLAB model is designed. Chapter 6provides the set up of this MATLAB model. Subsequently, scenarios are designed and specified inChapter 7. Consequently, results (i.e. the optimal sequence of turning a heat pump on or off) onthe different scenarios are shown and explained in Chapter 8. This thesis is evaluated in Chapter 9,where conclusions are drawn and limitations and future research opportunities are mentioned.

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2 UNIVERSAL SMART ENERGY FRAMEWORK

A short introduction concerning USEF was given previously in Section 1.1. In this Chapter a morethorough overview is presented. Firstly, an overview is given including, inter alia, the actors, theMarket-based Control Mechanism (MCM) and the operating regimes. Secondly an overview of thechanging role of the DSO is given. Moreover, the role of the DSO that is of interest for this thesis isdiscussed. All information presented here is derived from the USEF summary (2014) and the USEFspecifications (2015), unless stated otherwise.

2.1 Overview

USEF provides a framework of specifications, designs and implementation guidelines that allowsparticipants to create a fully functioning smart energy system. USEF enables the transition fromconsumers to prosumers while ensuring a safe, reliable, affordable and ever increasingly sustainableenergy system overarching the prosumers.

The prosumers, residential end-users and small and medium sized enterprises connected to the lowand medium voltage network, show an increasing amount of flexibility via demand response, themodification of prosumer’s load based on an external trigger. In combination with energy storageand local generation (e.g. via a µ-CHP) the envisioned smart grid holds more flexibility than everbefore. Flexible consumption is believed to be one way to compensate for energy systems withan increasing penetration of fluctuating sustainable energy sources (both in time and power) withrespect to grid stability (Biegel, 2014). USEF provides the framework in which this flexibility canbe accumulated, offered and obtained for grid capacity management and balancing of supply anddemand.

The observed increasing share of electricity as final form of energy will result in increasing peak loadson the system and require capital-intensive reinforcements of the grid. Historically, the network isdesigned to manage the peak load, a so-called fit and forget approach (Ecorys and ECN, 2014).Flexibility can be addressed to ease the peak load and defer or even avoid reinforcements, so-calledgrid capacity management. Imagine an increasing penetration rate of electrical vehicles that arebeing charged right after the end of an office day. In an uncontrolled, not smart, grid, this wouldcause severe stress on the transformer connecting the residential area with the grid. Smarter wayscould include the spreading of charging vehicles to lower the peak and prevent upgrades on thetransformer. Or imagine a highway that has to endure an increasing number of traffic in rush hour.Instead of adding additional, capital-intensive, lanes, a smarter way is to spread out the traffic overday by stimulating flexible working hours.

Besides, flexibility can be used for balancing supply and demand to seek the most economic dispatchpatterns and the overall lowest costs of the system as a whole. Generation costs can be reducedby, again, decreasing the peak load such that investments in generation capacity can be reduced.Moreover, the need for dispatching relatively expensive assets with high operational costs can bediminished. Balancing supply and demand prevents load curtailment. An abundance of sustainableenergy production can cause an oversupply that might result in system imbalances that requires thecurtailment of assets to prevent damage. Invoking additional demand in such periods shall avoidsuch undesired situations.

2.2 USEF actors

The transition from a top-down energy distribution grid to a bidirectional grid requires the intro-duction of new actors and changes in the roles of existing actors. Some of these actors are already

17

mentioned. In order to fully comprehend USEF and its MCM, an overview of these actors, theirroles and their interactions is presented. The actors active in an USEF compliant energy marketare graphically represented in Figure 1. The top half of this figure represent the energy value chainwhereas the lower half represents the physical system of the electricity system encompassing produc-ers, high and medium voltage transport networks, low voltage distribution networks and prosumers.The actors entitled in black are the actors currently active in the electricity market. The ones entitledin orange are new roles within the USEF compliant smart grid.

Figure 1: USEF interaction model of active actors. Copyright USEF Foundation (2015)

The producer produces energy and feeds it into the grid with the objective to produce at maximumefficiency. The traditional gas, coal and nuclear fuel based producers are confronted with an increasingpenetration of renewable energy producers characterised with low operation expenditures, like windand solar PV. Subsequently, prices will drop due to the merit order effect, resulting in implications onthe traditional fuel mix for electricity production (Paraschiv et al., 2014). The merit order effect isgraphically represented in Figure 2. The introduction of renewable energy sources with zero marginalcost will push the expensive conventional producers down the merit order and a preference lies withthe cheaper renewables. This effect lowers the prices and presents severe threats for the conventionalproducers. Moreover, Figure 2 shows the effect of decreasing demand due to the penetration of therenewables of which most is produced decentralised and consumed locally. Even though the effecton conventional producers is up to grasps, USEF emphasises the liberal nature of the market andleaves businesses free to combine roles in order to create a competitive advantage as long as thesecombinations are allowed within local regulations.

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Figure 2: The merit order effect (Clean Energy Wire, 2015).

The Transmission System Operator (TSO) transports energy from centralised energy producersover the high voltage grid and operates the interconnections with other voltage grids of neighbouringcountries. Moreover, the TSO maintains the system balance by deploying regulating capacity, reservecapacity and incidental emergency capacity. The role of the TSO is not affected by USEF.

The following three actors are new actors.

Prosumers are residential end-users and small and medium enterprises that actively up- and downloadenergy to and from the grid. The prosumers are the owners of the Active Demand & Supply.

Active Demand & Supply (ADS) represents all energy consuming and energy producing appliancesthat have the functionality to shift and to increase and decrease its energy consumption or production.The flexibility provided by the use of these appliances can be offered by the prosumer.

Aggregators accumulate the flexibility from the group of controlled prosumers and sells it to themarket. It is the goal of the aggregator to maximise the value of flexibility. It is evident that theaggregator has more bargaining power by accumulating flexibility among prosumers than a singleprosumer has, based on amount of flexibility that can be offered to the market. Therefore, theaggregator can negotiate on behalf of the prosumers with the market more efficiently (Gkatzikiset al., 2013). However, USEF allows for prosumers to directly access the market and thereby becometheir own aggregator which comes with responsibilities. The aggregator holds responsibility to takecustomer (i.e. the prosumer) needs, economical optimisation and grid capacity into account.

The Balance Responsible Party (BRP) is actively balancing supply and demand for its portfolioof producers, aggregators and prosumers in the most economical way based on forecasts of energydemand and supply. The BRP can directly source the producers or trade on the various energymarkets. This role is extended by procuring the available flexibility from the aggregators in orderto optimise its portfolio. In theory, the BRP can become an aggregator as well, however it has nomeans to exercise direct control over the user demand. Alternative means of indirect control suchas dynamic pricing is found to be challenging for a large number of prosumers and the fact that

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each only possesses a small amount of flexibility. This gives rise to the motivation of introducing theaggregator as mediator/broker (Gkatzikis et al., 2013).

The supplier sources, supplies and invoices energy to its customers. It shapes the financial side ofthe transaction within the electricity market. Consequently, it is the responsibility of the supplier toinvoice or reimburse the flexibility that is provided by prosumers.

The Energy Service Company (ESco) solely provides auxiliary energy-related services like insightservices or energy management services to prosumers and is neither directly active in the value chainnor in the physical system.

The Distribution System Operator (DSO) has the ability to perform grid management by cost-effectively distributing energy in a given area to and from end-users over the low voltage grid andthe connections to and from the high voltage grid. The goal of the DSO is to minimise grid capacitycosts while simultaneously safeguarding security of supply. If the limits of the distribution grid arereached, the yellow regime of USEF will be initialised and flexibility is procured from the aggregatorsto prevent expected congestion. If there is not enough flexibility available in the market, the orangeregime of USEF will be initialised. More on the operating regimes as defined by USEF can be foundin Section 2.3. Note the highlight on the term of system in Distribution System Operator as shownin Figure 1. The DSO within USEF is capable of managing the system by performing grid capacitymanagement. This is in contrast with the original Distribution Network Operator.

In Section 2.1, grid capacity management and the balancing of supply and demand are mentionedas goals for which flexibility can be accumulated and traded. USEF enables market parties tomaximise the value of this flexibility. Grid capacity management refers to the value of flexibility tothe DSO in order to shave the peak and prevent damage to components in the distribution grid.On the other hand, the BRP is interested in procuring the accumulated flexibility for the purpose ofbalancing demand and supply. The value chain of flexibility is depicted in Figure 3. In summary, theaccumulated flexibility of the prosumers can be traded between the aggregator and the DSO or theBRP.

Figure 3: Value chain of flexibility in USEF. Copyright USEF Foundation (2015)

Remark 1. Out of all actors present in USEF (Figure 1), Pons (2013) and Doddema (2014) solelyembed the aggregator, the BRP and the prosumer in their MPC application. Given the aim to embedthe DSO within these applications, the focus in this thesis lies merely on these 4 actors and theirinteraction in the value chain of USEF as depicted in Figure 3.

2.3 Market-based Control Mechanism

In order to maximise the value of the flexibility as provided by demand response, USEF’s maincomponent is the Market-based control Mechanism (MCM), an integrated market for all stakeholders.

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It is meant as an addition to the current liberalised market model built on the right to be connectedto the grid, the right to engage in energy transactions and the right to take and feed energy intothe grid at all times. The timescale of the electricity market runs down to the real time domainof minutes and rapid variations in supply and demand can be resolved with supply and demandbalancing. The aforementioned increase of intermittent renewable energy sources amplifies the needfor the MCM in order to operate the system in the most economical achievable way. With respectto the aforementioned operating regimes, the following responsibilities are defined:

The MCM distinguishes four operation regimes, of which two regimes represent the current affairsof a classic grid, and four operation phases. Figure 4 gives an overview of the setup of the MCM.Firstly an overview of the four operations regimes is given.

The green regime relates to normal operations in which the grid has enough capacity to distributethe energy demanded. In current business there is no functionality to reduce the load on the gridwhen the capacity of the grid is insufficient. To prevent damage to the infrastructure, in cases ofinsufficiency, the red regime of power outage is initialised. USEF adds two intermediate regimes, ayellow and orange regime. The yellow regime of grid capacity management involves the procurementof flexibility on both the demand and the supply side to ensure that peak loads remain within gridcapacity limits. The MCM enables this yellow regime. The green and yellow regimes establish thefree market and will act as the modus operandi in USEF compliant energy markets. In the exceptionalcase of reaching grid boundaries, the orange regime of graceful degradation is initialised. The MCMis overruled when it can no longer prevent congestion and grid connections are limited in order tore-establish the network load within acceptable limits, after which the free market can take overagain.

Figure 4: Market based Control Mechanism in USEF. Copyright USEF Foundation (2015)

The four operation phases are the plan phase, the validate phase, the operate phase and the settlephase. A short elaboration upon these phases follows hereafter and a more in-depth analysis ofdifferent phases follows in Sections 4.3 and 5.4, where respectively the initial model of Pons (2013)and the extended model are interpreted upon the fit with USEF. Moreover, in the light of this thesis,the focus lies primarily on the prosumer, the aggregator, the BRP and the DSO within the following

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short overview.

In the plan phase, supply and demand are forecasted by the aggregator and the DSO declarespossible locations within the distribution grid were congestion might occur, so called congestionpoints. Based on this information the aggregator optimises the portfolio of prosumers in order tomaximise the value of flexibility brought forward by the prosumers they represent. Moreover, aninteraction between the aggregator and the BRP ensures reaching the goal of this phase; to findan economically optimised program to supply the demand of energy of both the portfolio of theaggregators and the BRPs. This program is captured by the A-plan or Aggregator plan.

The validate phase is characterised by the aggregator creating so called D-prognoses of their pro-sumers per congestion point. The ADS is the linkage between the aggregator and the prosumerthat owns the ADS. The prosumers is free to engage with any aggregator. Therefore, there aremultiple aggregators active per congestion point. That is why the DSO collects and combines theD-prognoses of every aggregator in order to perform a grid safety analysis per congestion point. Thisanalysis determines whether the proposed distribution of electricity is feasible and within the limits ofthe distribution grid. If not, the yellow regime is enabled in order for the DSO to procure flexibility toprevent foreseen congestion. If there is not enough flexibility to do so, the orange regime of gracefuldegradation is enabled. Moving to the yellow regime would obviously alter the economic optimisationof the plan phase. Therefore, USEF defines these two phases to be iterative.

The two phases of plan and validate are finished and the A-plan and D-prognoses acts as startingpoint for the operate phase.

The operate phase encompasses the timeframe upon which the actual supply and demand ofelectricity takes place. However, the prognoses and validation of the previous phases may be alteredby deviations like changing weather conditions. The timeframe in which weather conditions candramatically change is substantial smaller then the timeframe in which electricity demand and supplyis forecasted, respectively 6-12 hours to 24 hours (van Werven and Scheepers, 2005). Deviationscause imbalances in supply and demand and possible local congestion. Therefore, additional flexibilitycan be traded between aggregators on the one side and the BRP or the DSO on the other side duringthe operation day.

The final settlement phase consists out of the actual financial settlement between all active parties.It encompasses the wholesale settlement between BRPs and prosumers, the transactions regardingprocured flexibility between the DSO and the aggregator and between the BRP and the aggrega-tor.

Remark 2. Pons (2013) demonstrates that MPC can be applied to the operation phase of the MCMwithin USEF for the green and yellow regime. Pons focuses solely on this phase since this is the onlyphase in USEF where real-time optimisation takes place.

In Chapter 4, MPC in general and the d-MPC application, applicable within the operate phase ofUSEFs MCM, in specific will be elaborated upon. This is followed by a thorough analysis of the fitof the application with the MCM to highlight what is included and what is excluded in the d-MPCapplication.

2.4 Changing role for the Distribution System Operator

In this thesis, the focus lies on the role of the DSO within the MCM. It is therefore illuminating toreview the changes brought along with the aforementioned transition to a smart grid.

The DSO is responsible for the cost-effective distribution of energy in a given area to and from end-users (i.e. prosumers) over the distribution grid. This distribution grid runs from the connections to

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the high-voltage transmission grid and the connections to the prosumers. Grid capacity management,based on the unleashed flexibility of the prosumers enables the DSO to minimise grid capacity costsand safeguard the security of supply in both the short and long term. The role of the DSO in thedifferent operating regimes is presented hereafter.

• Green regime. In the plan phase, the DSO identifies possible congestions points. In the validatephase, the DSO determines if congestion occurs given the optimised program as outcome of theinteraction between the BRP and the aggregator. During the operation phase, the DSO hasto monitor the stability of the grid at identified congestion points. Since there is no congestionin the green regime, there is no need for grid capacity management to prevent congestion.

• Yellow regime. In the validation phase the DSO buys flexibility from the aggregator to solveforeseeable congestion. In the operation phase, the DSO can buy additional flexibility toprevent unforeseen congestion in order for the system to not transit into the orange regime.The DSO is obliged to purchase all flexibility available to prevent a transition to the orangeregime.

• Orange regime. In the case of insufficient flexibility, the DSO has to sustain the highest servicelevel within capacity and safety limits by regulating the capacity of the connections.

• Red regime. In the case of an power outage, the roles of all actors in USEF in general do notdiffer from the current electricity system.

USEF specifies that a congestion point is a set of connections which are directly related to a partin the grid where capacity might exceed. For example, this might be a low voltage transformerconnecting the medium voltage grid to the distribution grid hosting the prosumers. It is not thetransformer that causes the congestion, but it is the point where the congestion, caused by theprosumers connected, accumulates and occurs. USEF defines congestion as capacity that mightexceed safety limits. It is up to the DSO to quantify congestion and safety limits in order to declareactual congestion points.

A consortium of Ecorys and the Energy research Centre of the Netherlands (2014) marks trends onboth the demand and supply side of the electricity network. On the demand side, the increase inelectrical vehicles and heat pumps will increase the demand significantly and become more variable.On the supply side an increase in distributed energy resources (e.g. the µ-CHP) and volatile renewableenergy sources (e.g. wind and solar PV) is foreseen. The increasing penetration of the latter willensure that the simultaneity factor increases. This factor captures the fact that the maximum load ona point in a distribution grid is smaller than the sum of the individual maximum loads connected tothat point (Oirsouw van, 2012). Specifically, it is the ratio of the simultaneous maximum demand ofa group of households to the sum of their individual maximum demand (Hemmingsson and Lexholm,2013). The distribution grid is not designed to the sum of the maximum load of each household,since those loads do not occur at the same time. This behaviour is captured by the equation ofRusck as described by Oirsouw (2012):

Pmax,n = g∞ · Pmax,l · n + (1 – g∞) · Pmax,l ·√n (1)

where the maximum load of n prosumers can be described by the maximum load of a single prosumerPmax,l and the simultaneity factor for an infinite amount of households g∞. In cold days the heatdemand will increase and prosumers will simultaneously turn on their heat pump. With an increasingnumber of heat pumps the simultaneity factor g∞ increases and thereby the maximum load of nprosumers that occurs at the low voltage transformer connecting these n households to the mediumvoltage network increases as well. On the demand side, the same happens with increasing numbersof installed solar PV, since the prosumers connected to a single transformer are geographically closelygrouped. The observed trends ensure that the limits of the transformer are going to be reached and

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congestion will occur. Andersen et al. (2012) defines congestion as a situation in which demandor supply of active power transfer exceeds the transfer capability of the distribution grid, in specificthe transformer. Oirsouw (2012) summarises by stating that the current networks without electricalvehicles, heat pumps, µ-CHPs and solar PV are designed based on the uneven spread of the loads.In future grids, including the previous mentioned technologies, only taking the uneven spread intoaccount will not suffice. Besides the stochastic behaviour of the prosumers, technologies with largersimultaneity factors should be accounted for.

In an interview with DSO professionals1 it came forward that the load increase on the transformer,due to an increase in simultaneity factors, and voltage control present the biggest challenges for theDSO to cope with in the transition to future smart grids.

Voltage control refers to ensuring that voltage variations do not exceed a regulated percentage (plusand minus 5 to 10%) of the nominal voltage. For example, electricity generation via solar PV panelsresults in high and unpredictable voltage levels. A complicating factor is that most of the solar poweris generated in summer daytime when the supply exceeds demand. Moreover, it is fed to a systemthat is designed upon the peak demand in winter time, which exceeds the peak demand in summertime (Hemmingsson and Lexholm, 2013).

Remark 3. In the light of the given d-MPC application, the focus in this thesis lies upon congestionmanagement at the low voltage transformer. By means of flexibility, the loads of prosumers at thetransformer can be regulated by shifting the loads in time. Consequently the simultaneity factorcan be lowered in order to meet the maximum capacity of the transformer. Thereby the notion ofcongestion as defined by USEF as capacity that might exceed safety limits is matched. Congestionmanagement thus refers to the procurement of flexibility by the DSO in order to prevent congestionand to remain in the yellow regime instead of shifting to the orange regime.

2.5 Distributed Model Predictive Control in USEF

In Remark 2 it is stated that the d-MPC application is applied to the operate phase of the MCM. Inthe d-MPC application, the A-plan and the D-prognosis from the plan and validate phase are capturedin the Day Ahead Planning (DAP), the forecast of supply to the group of prosumers controlled bythe aggregator. This planning acts as the desired trajectory for the prosumers of the aggregator.The d-MPC application and the DAP are explained in detail in Chapter 4. The applications acts asan internal optimisation tool for the aggregator to ensure that, by shifting the flexible loads of theprosumers, the DAP is followed as closely as possible. This all can be captured in the flow diagramdepicted in Figure 5.

1 Interview with Milo Broekmans from Stedin and Marcel Bogaerts from Alliander. Both Stedin and Alliander areDSOs in the Dutch electricity network.

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Day Ahead Planning

d-‐MPC Applica3on Aggregator

Op3mal Sequence of Flexible Loads

USEF Plan Phase &

USEF Validation Phase

USEF Operate Phase

Characteris3cs Prosumers

Informa3on Network

Characteris3cs Flexible Appliances

Capacity Constraints

Demand PaFerns

Capacity Constraints

Figure 5: Flow Diagram of the d-MPC application in USEF

The DAP, based on capacity constraints on the transformer and demand patters acts as the result ofthe plan and validation phase and as input for the d-MPC application. More detail on the DAP can befound in Subsections 4.2.2 and Section 5.3. Based on up-to-date information on the prosumers, theinformation network, the characteristics of the flexible appliances and the capacity constraints, theaggregator uses the d-MPC application in the operate phase of USEF to find the optimal sequence ofthe flexible appliances that minimises the offset with the DAP. The role of the DSO will be handledvia a market mechanism, where an economic signal as external trigger ensures that this optimalsequence the aggregator is looking for does not violate the capacity constraint of the transformer.Chapter 5 will explain this market mechanism.

In this chapter, USEF and the main component MCM are elaborated upon. The USEF framework isa given and the d-MPC application fits in the green and yellow regime of the operate phase. Moredetail on the fit of the given application with USEF will be given in Section 4.3.

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3 FLEXIBILITY

Flexibility is thus far mentioned as the ability to shift and increase or decrease supply or demand.In this chapter flexibility is defined and three different types of flexibility are investigated; bufferflexibility, time window flexibility and storage flexibility. Moreover, flexibility provided by a heatbuffer is quantified in order to be used for modelling purposes in Chapter 5.

3.1 Types of flexibilty

Roossien (2011) defines flexibility as the statistical interpretation of the shift-ability of the devicesin time within the boundaries of user comfort requirements and without changing its total energyproduction or consumption.

In this definition solely the ability to shift production or consumption in time is regarded as flexibility.So, modulation of power consumption or production is not regarded as flexibility since this wouldalter the output of a device. The consumption of a light bulb for example, can be altered by adding adimmer. However, the intensity of the light output from the light bulb then differs and the consumer’sexperience is affected. Roossien (2011) emphasises on those devices that can alter production orconsumption without changing the consumer’s experience. In the model of Doddema (2014) the heatpump is regarded as a flexible appliance. Such an appliance would fit the aforementioned definition.The heat pump, in combination with a heat buffer, can alter consumption forwards or backwardsin time without affecting the experience of the consumer. The user comfort requirements in thedefinition thus refers to the requirements on the heat buffer in the given example. This might be aminimum amount of litres of water at a specific temperature. As long as that requirement is met,the heat pump has the flexibility to shift in time. By doing so, the total consumption over time doesnot change. Flexibility is not only limited by the user requirements on comfort. When a heat bufferis full, the heat pump cannot operate any longer and all flexibility of the heat pump is gone.

Three different types of flexibility are elaborated upon by MacDougall et al. (2013).

1. Buffer flexibility refers to the flexibility provided by devices that buffer another commoditythan electricity. The heat pump in combination with a water storage tank that can store heatis an example of such an device. The flexibility of this system is thus limited by the buffercharacteristics on temperature settings and buffer capacity.

2. Time window flexibility refers to the flexibility of operation. A washing machine can shiftelectricity consumption within a given timeframe. Flexibility is thus provided by the timewindow available and the time the washing machine needs to run a certain program. Imaginea washing machine that can start operating any time during the night as long as the programis finished in the morning to be processed by the user.

3. Storage flexibility refers to, in contrast with buffer flexibility, direct storage of electricity. Thiscan for instance be a car battery.

The mentioned examples for the different types of flexibility hint on the availability of flexibility thatis still unused especially within the household sector. Flexibility elsewhere in the energy sector isalready mostly used (Roossien, 2011). Examples are large industries that can directly react uponrequest from the BRP. These industries contain a multitude of the flexibility that a single householdcan provide with a heat pump. It is however the number of households that compensates for the lackof individual flexibility. This relates to legitimacy of the aggregator as an accumulator of flexibilityto maximise the value, as described in Section 2.2.

Pons (2013) considered both µ-CHPs and heat pumps, both in combination with a heat buffer,whereas Doddema (2014) only considers the heat pump buffer combination. In this thesis the heat

27

pump is the only flexible device considered due to the focus on the DSO. In the next section, theflexibility provided by a heat pump is quantified.

3.2 Quantification of flexibility

The flexibility of the heat pump can be measured as the power increase or decrease with respectto a baseline (i.e. current) power consumption, that can be sustained for a given period of time.So, by shifting the operation of a heat pump of 1.1 kW one day ahead, the consumption at thecurrent day is decreased with 1.1 kW relative to the baseline whereas the consumption of tomorrowis increased with 1.1 kW. The total consumption over time thus does not change. Instead ofshifting consumption from today elsewhere, consumption can also be shifted from elsewhere towardstoday. It is defined that decreasing consumption today refers to ramping down whereas increasingconsumption today refers to ramping up. Based on the work of MacDougall et al. (2013) analyticaland numerical expressions of both ramp up and ramp down flexibility can be derived.

Since a heat pump can be connected to different sizes of thermal buffers, a normalised notation forthe buffer level is desirable. The buffer level at any given temperature T at time step τ is denotedby L(τ):

L(τ) =T – Tmin

Tmax – Tmin(2)

Note that the buffer level is characterised by the heat content of the buffer and not by the actualwater level in the buffer. It is thus assumed that the water level remains constant during filling anddraining of the buffer and solely the heat content of the buffer is changing. Given the definition offlexibility as a power increase or decrease relative to a baseline, two scenarios can be set apart. Whenthe heat pump is turned on it can be turned off, and when the heat pump is turned off it can beturned on. Both scenarios are described hereafter:

3.2.1 Ramp up flexibility

When the heat pump is off it can be turned on such that the buffer fills up to L(τ) = 1. The heatpump ramps up and ensures an increase in electricity consumption of the household with respect tothe baseline (i.e. the heat pump is off and does not consume electricity). The buffer fills accordingto

L(τ) = L0 +α

C· Pnom · τ (3)

where L0 is the initial buffer level at L(τ)|τ=0 and α reflects the ratio between electric and thermalpower. Electrical power is converted to thermal power for a period of τ minutes. The heat pumpconsumes Pnom = 1.1 kW in order to produce 3.3 kW of heat. αHP = 900 kJ/kW, meaning thatfor every kW of input per time step of τ = 5 minutes, 900 kJ is added to the heat buffer. C reflectsthe conversion factor from thermal power to the buffer level and thus relates to the maximum heatcontent of the thermal buffer. The thermal buffer of interest has the following characteristics withrespect to the maximum temperature the buffer can hold.

C = volume [m3] · heat capacity of water [kJ · kg–1 ·K–1]·density of water [kg ·m–3] · temperature difference [K]

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Given the specifications of the heat buffer as used by both Pons (2013) and Doddema (2014), thatis Tmin = 20◦C, Tmax = 45◦C and a buffer capacity of 120 L results in C = 12.558 MJ.

The heat pump cannot modulate in the power consumption Pn, and thus

Pn = 0 kW ∨ Pn = Pnom = 1.1 kW

which means that the heat pump stores αHP · Pnom, equals 1.1 kW · 900 kJ/kW = 990 kJ everytime step of operation.

Based on the work of MacDougall et al. (2013) the following expression for the ramp up flexibilityF+(τ) of the heat pump can be defined as

F+(τ) = min

((Noff · C(1 – L0)

αHP · τ

), (Pn – Pnom)

)(4)

with Noff equals 1 when the heat pump is off and 0 when the heat pump is on.

Using equation (4), the flexibility of an individual heat pump. Figure 6 shows the interpretation ofequation (4).

Figure 6: Ramp up flexibility of the heat pump

The first term of the minimisation function in equation (4), the green plot in Figure 6, depicts theelectrical capacity still available in the buffer. The total electrical capacity of a single buffer perheat pump equals (12558 kJ / 900 kJ/kW) = 13.95 kW, which ensures that a 1.1 kW heat pumpneeds a theoretical 12.7 time steps to fill the buffer, neglecting heat demand and heat losses thatwill drain the buffer. The second term of equation (4), the blue plot in Figure 6, depicts the rampup potential of an amount of N heat pumps and takes the average power, depicting how many heatpumps are in fact able to be turned on, into account. The first and second term intersect at exactlythe some moment when the heat buffer is full (i.e. at 12.7 time steps). Before the buffer is full, thesecond term is the smallest and indeed, the heat pump can continue to fill the buffer with a rampup flexibility of Ntot(Pnom – Pavg) = 1(1.1 – 0) = 1.1 kW. After the buffer is full, the first termbecomes the minimum and the ramp up flexibility is depicted by this same term. For a single heatpump, equation (4) yields the ramp up flexibility as presented in Table 1.

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Table 1: Ramp up flexibility of a single heat pump

τ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15kW 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.073 0.997 0.930

A ramp up of 1.1 kW is able to be sustained for 12 time steps after which the buffer is full. Atheoretical ramp up of 0.997 kW is able to be sustained for 14 time steps. Since we assumed thatthe heat pump cannot modulate in power, but solely can be turned on or off, an increase in electricityconsumption of 0.997 kW is not possible.

By rewriting equation (4), the time at which the buffer is full can analytically be determined by

τ =Noff · C(1 – L0)

(Pnom – Pn) · αHP(5)

3.2.2 Ramp down flexibility

When the heat pump is in operation, it can be switched off. Subsequently the buffer will drain untilthe buffer is depleted after which the heat pump should be switched on again. MacDougall et al.(2013) assumes that the buffer drains at the same rate as which it filled in the case of turning theheat pump on. By doing so, the following equations can be derived.

When switching off the heat pump, the electricity consumption decreases compared to the baseline inwhich the heat pump was still in operation. The ramp down flexibility F–(τ) can be derived by

F–(τ) = max

((–Non · C · L0αHP · τ

), –(Pn)

)(6)

with Non equals 1 when the heat pump is on and 0 when the heat pump is off.

and the time of depletion after rewriting equation (6) can be derived by

τ =–Non · C · L0F– · αHP

(7)

In contrast to draining the heat buffer by a fixed rate as shown before, it is more realistic to drainthe heat buffer by the actual demand from the household. Subsequently, analytical expressions areno longer obtainable and the solution of equation 6 is ought to be found numerically.

For a single heat pump, the results for both ramp up and ramp down flexibility are presented inFigure 7, depicting the ramp power and the associated time for which that amount of power can besustained.

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-‐1.5

-‐1

-‐0.5

0

0.5

1

1.5

0 100 200 300 400 500 600 700 800 F(τ) [kW]

Time [minutes]

HP Ramp up HP Ramp down

Figure 7: Heat pump ramp up and ramp down flexibility

It can clearly be seen that when the buffer is being filled the heat pump’s ramp up flexibility showssmooth results. When the buffer is drained after turning the devices off, non-smooth results areobtained as a result of a heat demand pattern that ensures that not analytical expressions but solelynumerical solutions can be obtained. In Section 5.3, the general notation on quantifying flexibility aspresented here is modified to fit the model at hand in order to be used as a tool to divide the DAPinto individual goal functions based on the amount of flexibility a prosumer possesses. The notionof DAP and individual goal functions is elaborated upon in Subsection 4.2.2.

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4 MODEL PREDICTIVE CONTROL IN SMART GRIDS

In this chapter the general form of a MPC problem is presented, as well as the centralised anddistributed applications as described by Pons (2013), that fits the operate phase of MCM withinUSEF. The use of the Day Ahead Planning is explained and in Section 4.3, the fit of the d-MPC inUSEF is described in detail. The embedding of the DSO is explained in Chapter 5 hereafter.

4.1 Model Predictive Control

MPC is a control methodology that, based on a dynamical system and future predictions, computesan optimal trajectory. The notion of optimality relates to the objective function of the problemand can, for example, refer to the maximisation of a profit function, the minimisation of a costfunction or even the pursuing of a pre-arranged desired trajectory (Halvgaard, 2014). d-MPC isfound to be an useful method to coordinate decisions in a smart grid and provides easy handling ofconstraints (Larsen, 2014). Hereafter, MPC and specifically d-MPC as optimal control methodologyare elaborated upon.

First we show the general form of a centralised MPC problem. In a network of n nodes where everynode i at time step (k) is defined by state xi(k), control input ui(k) and disturbance wi(k) we definea quadratic objective function as

Vi(k) = |x(k)|2Q + |ui(k)|2R (8)

The first term in equation (8) represents a weight Q on state xi(k) and the second term resemblesa penalty, with weight R, on excessive use of this control input ui(k). The dynamic state equation,in compact form, is defined as

xi(k + 1) = Axi(k) + Bu(k) + w(k) (9)

where

x(k) = [xi(k) . . . xn(k)]T

u(k) = [ui(k) . . . un(k)]T

w(k) = [wi(k) . . .wn(k)]T

(10)

in order to group the sequence of, respectively, the state, the control input and the disturbance ofthe prosumers. The idea of MPC is to solve for each time step k a control problem over a finiteprediction horizon denoted by τ = [k, k + Kpred] ∈ R. Subsequently, only the first control inputui(τ)|τ=k of the future input trajectory is implemented. For the next time step k + 1 a new controlproblem is solved over the shifted prediction horizon τ = [k+1, k+1+Kpred] and again only the firstcontrol input is chosen. By applying this methodology for each time step k, the original optimisationproblem from k = 0 to k = T is ought to be solved. Since the prediction horizon remains of thelength Kpred and solely shifts forward at each time step k, this form of control is often referred toas receding horizon control (Maciejowski, 2000). Figure 8, represents the previous graphically. Itshows how, with the use of the receding horizon principle, the control inputs ui steer the state xi toa desired target trajectory.

33

Figure 8: Graphic representation of the receding horizon principle (Doddema, 2014).

Minimising the objective function from equation (8) over the optimisation horizon k = [0, T] resultsin the following control problem to be solved (Larsen, 2014).

minimiseu

T∑k=0

k+Kpred∑τ=k

Vi(τ)

subject to

xi(k + 1) = Ax(k) + Bu(k) + w(k)

(11)

4.2 Distributed Model Predictive Control as Market-based Control Mechanism

With respect to the problem setting of the MCM within the USEF framework, the previous generalnotation can be adapted. Based on previous work by (Larsen, 2014), (Pons, 2013) and (Doddema,2014) the problem can be defined. Our system of interest consists out of 1 BRP hosting l = 1, . . . , maggregators. i = 1, . . . , nl nodes representing households or prosumers are specifically assigned to asingle aggregator l. The network topology of this multi-agent system is graphically represented inFigure 9.

25

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Supplier

BalanceResponsible

Party

TransmissionSystem

Operator DistributionSystem

Operator

Producer

Supply

ESCo

AggregatorProsumer

Active-Demand & Supply

tradeenergy

control usersettings

provide auxiliaryservices

provideenergy

supplyenergy

demand responseframework agreementdispatch

power plantsupply flexibility

for portfoliooptimization

control demandresponse

supply flexibilityfor grid capacity

managementtransportenergy

transportenergy

distributeenergy

energy & demandresponse contract

3567kWh

kWhkW

these settings may influence the flexibility these appliances

and assets can provide to the Aggregator.

BRP and Supplier (N-to-M)

The Supplier has a contract with the BRP that defines

the commercial terms under which the BRP sources

the energy demand and supply of the Prosumers under

contract with the Supplier. This contract, which is already

in place in the current liberalized energy market, is not

affected by USEF.

BRP and Aggregator (N-to-M)

The Aggregator and BRP negotiate how to mutually

optimize their portfolios and identify the lowest operational

costs. Flexibility is traded according to the MCM. Although

in general an Aggregator can interact with multiple BRPs,

an Aggregator can only interact with a single BRP for any

given connection. This BRP must be the same BRP that

provides energy to the Supplier with whom the Aggregator

has a framework agreement for that connection.

BRP and Producer (N-to-M)

Based on its portfolio optimization, the BRP determines the

most economical way to balance its portfolio. This process

determines how much energy each power plant should

produce in the upcoming period. The BRP orders the

Producer to dispatch that amount of energy in the upcoming

period or purchases it on the market. In the Operate phase

(see chapter 8), the BRP can ask the Producer to alter its

production plan. This process, which is already in place in the

current liberalized energy market, is not affected by USEF.

TSO and BRP (1-to-N)15

The TSO validates whether the energy transport planned

by all the BRPs (in their E-programs) can be executed

reliably and safely. The TSO continuously monitors network

conditions and, when imbalances arise, buys regulating

power from the BRPs to balance the system.

Figure 10: The USEF interaction model, including the most important contractual relationships.

13 Although third parties can serve as energy resellers under the auspices

of the Supplier’s supply permit, the responsibilities remain with the Supplier.

14 The reasoning behind this is that commodity and flexibility are inherently linked

to one another, and hence also the settlement of commodity and flexibility.

This becomes even more apparent when time-of-use tariffs are applied.

15 Assuming there is only one TSO active in the country. If multiple TSOs

are present, the relationship would be N-to-M. This also holds true for the

TSO-DSO interaction.

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i=1 i=n1 i=n2 i=nm i=1 i=1

Figure 9: Network topology consisting out of a single BRP, n aggregators and nl prosumers.

The physical electricity imbalance of a single prosumer is quantified by the summation of the fixed(non-flexible) and flexible electrical load, each composed of either electricity producing or consumingdevices. Thus, 4 types of devices are distinguished; a flexible electricity consuming device (e.g. a heat

34

pump), a fixed electricity consuming device (e.g. the television), a flexible electricity producing device(e.g. a µ-CHP) and a fixed electricity producing device (e.g. solar photovoltaics panels).

Let gi(k) and f i(k) represent, respectively the fixed and flexible load of prosumer i at time k.Consequently, the physical electricity imbalance xi(k) at time k equals

xi(k) = gi(k) + f i(k) for i = 1, . . . , nl (12)

and represents the offset between consumption and production of a single prosumers i at time (k).We define

gi(k) < 0 if fixed production > fixed consumptiongi(k) > 0 if fixed production < fixed consumption

(13)

and likewise for the flexible load f i(k). Thus, xi(k) < 0 represents a net producer whereas xi(k) > 0represent a net consumer and xi(k) = 0 represents an energy neutral household.

The aggregator accumulates the loads and imbalances of the individual prosumers it is consisting ofand thus

gag(k) =nl∑i=1

gi(k) l = 1, . . . , n fixed load of aggregator node l at time k

fag(k) =nl∑i=1

f i(k) l = 1, . . . , n flexible load of aggregator node l at time k

xag,l(k) =nl∑i=1

xi(k) l = 1, . . . , n physical electricity imbalance of aggregator node l

(14)

Translating the general notion of equations (8) and (11), the central optimisation problem of theBRP is defined as the minimisation of the total physical electrical imbalance x. The central objectivefunction is thus:

V(τ) =T∑

k=0

k+Kpred∑τ=k

∣∣∣∣∣n∑

l=1

ˆxag,l(τ)∣∣∣∣∣2

Q

+∣∣∣4f(τ)

∣∣∣2R

(15)

with4f i(τ) = f i(τ + 1) – f i(τ)

A hat notation is used to indicate predictions of the state xi(τ) and the change in input 4f in theprediction horizon of the d-MPC strategy.

The idea is to use the flexibility provided by the flexible devices, captured by f(k). With a MPCalgorithm the sequence of f(k) over k = [0, T] that minimises total physical imbalance is sought for.A MPC strategy that ensures a centralised optimisation is however undesirable. First of all, in generalit would require that local data of prosumers should be communicated to, and be hold by, a centralcontroller. In specific, in the competitive nature of the energy market, the sharing of informationamong all prosumers and aggregators is not likely (Biegel et al., 2012a). Besides, an overwhelmingnumber of decision variables are ought to be found by a single controller. A centralised optimisationproblem as in equation (15) is intractable (Doddema, 2014).

35

In order to solve the central optimisation problem in a large-scale network of aggregators and pro-sumers, a common approach is that of designing decentralised controllers (Giselsson and Rantzer,2010). Thereby, a single centralised problem is split over the network, such that each agent withinthat network can solve their own distributed problem with only local information (Larsen, 2014).Decomposition is an approach to solving a centralised problem by breaking that problem up intosmaller problems and solve the smaller problems separately (Boyd et al., 2003). The centralisedobjective function (15) ought to be decomposed to a distributed Model Predictive Control (d-MPC)problem where nodes make fully decentralised decisions for their own flexible appliances by alteringtheir flexible load f i. The part of the centralised objective function for each prosumer i is definedas

Vi(k) =

k+Kpred∑τ=k

|xi(τ)|2Qi+∣∣∣4f i(τ)

∣∣∣2Ri

(16)

Note that in equation (16) is referred to xi(τ), or the informational imbalance rather then the physicalimbalance x considered in equation (15).This informational imbalance reflects the imbalance that isshared among prosumers. The next section reflects on this informational imbalance that couples thethe prosumers.

4.2.1 Coupling of prosumers

In order to solve the decentralised objective function per prosumer we require a state equation thatdynamically couples prosumers. The dynamic state equation is given by

xi(τ + 1) = Aiixi(τ) +∑j 6=i

Aijxj(τ) +4f i(τ) +4gi(τ) ∀τ (17)

This dynamic state equation, relating the future state xi(τ + 1), the current input f i(τ) and thecurrent state xi(τ), couples the prosumers within the portfolio of an aggregator. Prosumer i isdynamically coupled to its neighbour, prosumer j, via shared imbalance by a weight Aij given by theinformation matrix A. Larsen (2014) defines 4 requirements on the information matrix A in order tobe stable and to conserve total informational imbalance.

1. Aij 6= 0 if and only if information is exchanged between prosumer i and j.

2. All weights are non-negative: Aij > 0, i, j = 1, . . . , n.

3. All columns sum up equal to one:n∑

i=1

Aij = 1, . . . , n.

4. The graph corresponding to information matrix A is strongly connected, which means thatthere is a path from any prosumer to any prosumer.

Given these requirements, the total informational imbalance in the network equals the total physicalimbalance in the network. However, the individual physical imbalance xi is not equal to the individualinformational imbalance xi.

n∑i=1

xi(k) =n∑

i=1

xi(k) ∀k ≥ 0. (18)

36

The future state xi(τ + 1) depends on the own previous imbalance xi(τ) of prosumer i, a weightedportion of the imbalance of neighbours j, the change in input denoted by 4f i(τ), and the change infixed uncontrollable load 4gi(τ).

4gi(τ) = gi(τ + 1) – gi(τ)

Each prosumer addresses its own flexible appliances to minimise the individual informational imbal-ance from equation (16).

The problem from equation (16) can not be easily split in multiple subproblems since the dynamicstate equation from (17) couples prosumers via their shared informational imbalance. Dual decom-position is required to split the complicating variable (i.e. the variable that couples the problem) intolocal versions (Boyd et al., 2003). Adapted to our problem, each prosumer i introduces a variablevi(τ) in its own state equation to represent the expected imbalance from neighbour j. Consequently,the dynamic state equation can be rewritten to

xi(τ + 1) = Aiixi(τ) + vi(τ) +4f i(τ) +4gi(τ) ∀τ (19)

with

vi(τ) =∑j 6=i

Aijxj(τ) (20)

The equality constraint from (20) represents the expected influence of connected neighbour j onprosumer i and is incorporated in the decentralised objective function via a dual variable, or aLagrange multiplier, λi. Subsequently, equation (16) becomes

Vi(k) =

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri

+ λi(τ)

(vi(τ) –

∑j6=i

Aijxj(τ)

))(21)

which consequently leads to the following, fully decoupled objective function

Vi(k) =

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri

+ λi(τ)vi(τ) – xi(τ)

(∑j6=i

Ajiλj(τ)

))(22)

where the Lagrange multipliers λi and λj act as price signals between neighbours. The primal problemof equation (15) is split into several smaller dual problems via Lagrange relaxation in which violationof the equality constraint (20) is penalised by means of a Lagrange multiplier in the decentralisedobjective function (23). As a result each prosumer i can minimise the objective function that solelydepends on local information and price signals of connecting neighbours.

minf i

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri


(∑j 6=i

Ajiλj(τ)

))(23)

37

By maximising over the the Lagrange multipliers, the best lower bound on the optimal value of theprimal problem is obtained (Larsen, 2014). The following problem to be solved is

maxλ

n∑i=1

minf i

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri


(∑j 6=i

Ajiλj(τ)

))(24)

subject to

xi(τ + 1) = Aiixi(k) + vi(τ) +4f i(τ) +4gi(τ) ∀τ (25)

Nedíc and Ozdaglar (2009) distinguish two parts to be specified in a multi-agent optimisation problem.An information exchange part in which the agents share information among each other in order forindividual agents to minimise an agent-specific objective function in a optimisation model embodiesthe first part, or the inner optimisation. With problem (24) at hand, an inner optimisation, hostingthe minimisation of the objective function (23) and an outer optimisation model, the second part, inwhich the Lagrange multipliers are ought to be found can be distinguished (Doddema, 2014).

Finding the appropriate Lagrange multipliers requires a sub-gradient method such that (24) is ap-proximated. (Larsen, 2014).

At every iteration step r, the Lagrange multipliers are updated as follows

λi,r+1(τ) = λi,r(τ) + γi,r

(vi,r(τ) –

∑j6=i

Aijxj,r(τ)

)(26)

such that the expected influence vi(τ) approaches the actual information imbalance∑j 6=i

Aijxj. The

sub-gradient method is terminated when the update is converged to a threshold ε for practicalreasons. As Doddema (2014) mentions, ideally the sub-gradient continues until all prosumers reachedconsensus with their connected neighbours.

4.2.2 Day Ahead Planning

Recall that the BRP actively balances supply and demand for its portfolio of aggregators in the mosteconomical way based on forecasts of demand and supply. Therefore, the BRP defines a Day AheadPlanning (DAP) as a desired target trajectory. Aggregators address the flexible electricity devicesof the prosumers within their portfolio to conform to this desired trajectory. Pons (2013) redefinesequation (25) to

xi(τ + 1) = Aiixi(τ) + vi(τ) +4f i(τ) +4gi(τ) –4goali(τ) ∀τ (27)

where

4goali(τ) = goali(τ + 1) – goali(τ)

A local goal function is incorporated in equation (27). Thereby, the DAP is split up in parts such thateach prosumer i can contribute to the main goal without being coupled to other prosumers.

As a result a distributed MPC is obtained in which prosumers can solve their own minimisationproblem by using only local information, the informational imbalance and the Lagrange multiplier ofneighbours. This in contrast to a centralised MPC where the central controller requires information

38

off all the prosumers within the network. Note that only a central controller is needed to actuallydivide the DAP into prosumer specific goal functions.

Larsen (2014) shows that, whenever the problem is convex, the solution of Algorithm 1 converges tothe solution of the primal problem. In that case, the duality gap, the difference between the solutionof the dual problem from equation (24) and the solution of the primal problem from equation (15),equals zero and strong duality holds.

Result: Find 4f i(k) at each cycle k of the distributed MPC methodfor k = 0, . . . , T do

each prosumer i measures xi(k),wi(k);while

∣∣∣λi,r(τ) – λi,r–1(τ)∣∣∣ > ε dofor i = 1, . . . , n do

solve (23);endeach prosumer i communicates {xi(τ)}

k+Kpred

τ=k to connected prosumers;for i = 1, . . . , n do

sub-gradient update (26);endeach prosumer i communicates {λi(τ)}

k+Kpred

τ=k to connected prosumers;endeach prosumer i implements 4f i(k) = 4f i(τ)|τ=k;

endAlgorithm 1: Distributed Model Predictive Control, after Larsen (2014).

4.3 USEF interpretation

Pons (2013) shows that MPC can be used within the operate phase of USEF (Remark 2). Within hisspecific application, the BRP, the aggregators and the prosumers cooperate to minimise imbalancein the system. Pons focuses solely on this phase since this is the only phase in USEF where real-timeoptimisation takes place. Moreover, the model by Pons only relates to the green and yellow regime ofthe operation phase where the BRP requests flexibility to minimise imbalance. Input for the d-MPCapplication in the operate phase is the DAP, the result of the plan and validation phase.

Figure 10 depicts the validation phase of USEF. Highlighted in the black box is the decision of theDSO to stay in the green regime or to move to the yellow or orange regime. At decision node1, based on the D-prognoses, the DSO is able to determine whether this prognoses will lead tocongestion or not. If it does not, the plan is validated and USEF remains in the green regime. Ifit does and congestion is expected, the DSO has to determine when the congestion is expectedand how much flexibility is required to prevent the foreseen congestion. In USEF it is known howmuch flexibility is available. At decision node 2 it is determined whether this amount is enough toprevent the foreseen congestion. If so, the yellow regime will be enabled in which the DSO and theaggregator trade flexibility. If there is not enough flexibility available, the orange regime is enabledand the DSO will have to lower connections in the upcoming operate phase to prevent damage tothe infrastructure.

In Section 2.5 it was analysed that in the application of Pons (2013), the Day Ahead Planning (DAP)is the result of the plan and validation phase and serves as input for the d-MPC application. TheDAP represents the electricity as bought by the BRP for the next day. Subsequently, the algorithmensures that this planning, or desired trajectory in MPC terms, is followed. The BRP desires tominimise the imbalance costs, that is the costs associated with the imbalance between the totaldemand and the total supply represented by the DAP. This relates to the physical imbalance x. The

39

model is designed to minimise the informational imbalance x. However, the requirements on theinformation matrix A as described in Subsection 4.2.1 ensures that the total informational imbalanceequals the physical imbalance as shown in equation (18). More on the performance indicators andthe desire of the BRP to minimise the total physical imbalance x can be found in Section 6.6

Remark 4. In the d-MPC application it is assumed that the validate phase is concluded with avalidated plan, a DAP, without foreseen congestion. From Figure 10, this is either the result froma D-prognoses that does not contain any congestion (answer no at decision node 1) or from anadjusted plan as result from flexibility trading in the yellow regime (answer yes at decision node 2).In both cases, the DAP is a planning free of congestion that the aggregator desires to follow as closeas possible in the operate phase by means of internal optimisation via d-MPC.

How it is ensured that the DAP is free of congestion is explained in Section 5.4.

Figure 10: Process flow of the USEF validate phase. Copyright USEF Foundation (2015)

Previously, a short overview of the operate phase was given. In Figure 11, the flow diagram of theoperate phase as defined by USEF is illustrated. The operate phase is characterised by the BRPand the DSO both placing flexibility orders at the aggregator. The BRP desires so in order to copewith changing market circumstances with respect to balancing supply and demand, whereas the DSOrequests flexibility to prevent congestion that was not foreseen in the plan and validation phases.The aggregator constantly re-optimises its portfolio to maximise the value of the flexibility of theADS owned by the prosumers and to follow the desired DAP as close as possible.

Remark 5. During the operate phase and in the case of changing market circumstances the BRPmight desire the aggregator to follow an adjusted DAP. MPC allows for changing the desired tra-jectory during the optimisation. In this thesis the DAP is assumed to be static, free of congestionand known before the start of the operate phase. The DAP thereby acts as the input for the d-MPCalgorithm.

The aggregator thus receives a static DAP that is free of congestion. By means of shifting theflexible loads of the prosumers in time, the aggregator desires to minimise the imbalance with theDAP.

Pons (2013) thus includes all the actors active in this phase except for the DSO which is highlightedin the black box in Figure 11. Pons (2013) narrowed down the scope by addressing a single BRPin order to exclude the imbalance market that allows for trading of electricity during the operationphase among BRPs.

40

Figure 11: Process flow of the USEF operate phase. Copyright USEF Foundation (2015)

In Chapter 5, hereafter, the design of the model that includes the DSO will be explained. In Section5.4 the role of the DSO is elaborated upon with respect to the fit with USEF.

41

5 DISTRIBUTED MODEL PREDICTIVE CONTROL INCLUDINGTHE DSO

In Chapter 4 the d-MPC, suitable as control algorithm in the operate phase of the MCM as definedby USEF, is presented. Moreover, it was pointed out that of all actors active in the operate phase,the DSO is the only actor lacking in the d-MPC model.

A market-mechanism is necessary to ensure that the transformer is not constrained and that USEFdoes not shift towards the orange regime of graceful degradation in order to prevent damage on as-sets. The d-MPC acts as an internal optimisation tool for the aggregator to ensure that the desiredtrajectory of the DAP is reached and that the total load at the transformer does not violate the loadconstraint during the operate phase of USEF. Moreover it enables the prevention of unforeseen con-gestion during the operate phase that might occur due to, for example, changing weather conditions.If the algorithm is not able to find a sequence that prevents congestion, the aggregator and the DSOwill have to financially settle in the USEF phase of settlement. This phase is outside the scope ofthis thesis.

In this chapter, the role of the DSO as explained in Section 2.4 will be translated in order to besuitable for adding to the existing model. Consequently, the model will enable solving congestionduring the operate phase and prevent a shift towards the orange regime.

5.1 Congestion management

Liu it et al. (2014) identify three categories of congestion management strategies. Switch operationrefers to reconfiguring the system such that congestion is altered but is not very effective in radialnetworks. The low voltage distribution network is primarily radially designed (Oirsouw van, 2012).Moreover, such a strategy does not use the unleashed flexibility provided by appliances such as heatpumps and µ-CHPs. Congestion is more effectively handled through demand response (Liu et al.,2014). Demand response is the modification of a user load, based on an external trigger (DNV-GL,2015). The second and third category as identified by Liu it et al. (2014) are considered as demandresponse strategies. The external trigger can either be a direct signal that alters the load, so calleddirect load control, or via a market mechanism. In the latter case, the external trigger is a marketprice or an economic signal directing the behaviour of flexible loads. Andersen et al. (2012) identifiesthree algorithms for congestion management based on demand response via market prices that differin complexity and effectiveness. The model as presented in Chapter 4 does not include marketprices. It is therefore evident that a congestion management strategy based on demand response viaa market mechanism and an economic signal, rather than a market price, is a logical choice.

5.2 Congestion management via Lagrange multipliers

In Section 2.4, congestion management by procuring flexibility was referred to as a tool for the DSOto prevent congestion on the low voltage transformer connecting the prosumers in the low voltagedistribution grid to the rest of the electricity grid. By shifting flexible loads in time, the total loadof a group of prosumers can be altered and thereby regulated to a given load constraint on thetransformer.

43

Given the mathematical notation as presented in Chapter 4, the total load at a transformer at timek can be defined as the sum of the flexible and fixed load of all prosumers i connected to transformerz.

Ltransformer(k) =∑i∈z

(f i(k) + gi(k)

)(28)

The total load on the transformer should be regulated in order to not violate the capacity constraintLmax of transformer z. Therefore,

∑i∈z

(f i(k) + gi(k)

)≤ Lz,max (29)

This inequality constraint on the transformer couples the distributed problem of (24) back to acentralised problem, since the summation of the load off all prosumers connected to the transformerdetermines the load on the transformer. In order to define an objective function that is fully decoupledsuch that every prosumer can solve an individual problem without sharing the fixed and flexible load,the same analogy of decoupling is used in Subsection 4.2.1 where prosumers who share informationalimbalances among each other were decoupled via dual decomposition. By introducing a secondLagrange multiplier µ a fully decoupled objective function can be guaranteed.

Vi(k) =

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri


(∑j 6=i

Ajiλj(τ)

)

+ µz(τ)

(f i(τ) + gi(τ)

)) (30)

The complicating variable Lz,max, (i.e. the variable that couples the problem), from equation (29) isno longer present in the objective function of equation (30). It is therefore that this objective functioncan be minimised by each prosumer individually since only the individual load (the sum of fixed loadf i(τ) and flexible load gi(τ)) of prosumer i is considered. λj is a prosumer specific Lagrange multiplierassociated with the expected influence of prosumer j upon prosumer i. The sum

∑j 6=i

Ajiλj(τ) is the

accumulation of all prosumers j that are connected to, and thus influence, prosumer i. In the settingof congestion management however, the Lagrange multiplier µ is not prosumer specific but rathertransformer specific. All prosumers connected to transformer z will receive a Lagrange multipliermuz based upon the total load on this transformer z. The sum of the loads

∑i∈z

from equation (29) is

subsequently determined in the update of muz in the sub-gradient method described hereafter.

The objective function from equation (30) now consists out of 2 Lagrange multipliers. The firstLagrange multiplier λ refers to the expected influence of connected neighbours and the secondLagrange multiplier µ refers to the load on transformer z.

Following the same procedure to obtain equation (24), the following problem that incorporates

44

congestion management can be defined:

maxλ,µ

n∑i=1

minf i

k+Kpred∑τ=k

(|xi(τ)|2Qi

+∣∣∣4f i(τ)

∣∣∣2Ri


(∑j6=i

Ajiλj(τ)

)

+ µz(τ )f i(τ) + µz(τ)gi(τ)

) (31)

subject to

xi(τ + 1) = Aiixi(τ) + vi(τ) +4f i(τ) +4gi(τ) –4goali(τ) ∀τ (32)

Finding the appropriate Lagrange multipliers µ requires a second sub-gradient method.

Based on Biegel (2012a) µz will be updated at every iteration step r according to

µz,r+1(τ) = max[0,µz,r + γi,r

(∑i∈z

(f i(τ) + gi(τ)

)– Lz,max(τ)

)](33)

When all prosumers solved problem (31) the algorithm will compute µi,r+1(τ) based on the totalload (i.e. the sum of the loads of the current iteration r of prosumers i that are connected totransformer z) and the maximum load Lz,max as specified for transformer z. When the total load∑i∈z

(f i(τ) + gi(τ)

)exceeds the maximum permissible load at the transformer (Lz,max) the term∑

i∈z

(f i(τ) + gi(τ)

)– Lz,max(τ) becomes positive and given a strictly positive growth rate γi,r the

shadow prices will increase with a positive update. Considering the prediction horizon, the time stepτ at which the capacity constraint at the transformer is violated will receive a positive µi,r+1(τ).This Lagrange multiplier, or shadow price acts as a penalty on the objective function (30). Thepenalty will ensure that the d-MPC will alter the use of the flexible device to another time step inwhich the capacity constraint will not be violated, subsequently a penalty is circumvented and theobjective function is minimised. This penalty does not reflect a market price, but merely an economicsignal.

Note the max statement to ensure that the shadow price µ is strictly positive. Thereby solely the useof flexible load at those time steps at which violation of the constraint occurs is discouraged, ratherthen also encouraging (rewarding) the use of flexible load at time steps at which the constraint is notviolated. Strictly discouraging rather than both discouraging and encouraging proved to increase theperformance of the model to find feasible solutions. The sub-gradient method is terminated when atall time steps within the prediction horizon the capacity constraint of the transformer is not violatedor when a maximum number of iterations is reached. The model can only alter flexible load withinthe prediction horizon. Remark that congestion cannot be prevented if there is no sequence of controlinputs possible that would result into a feasible solution. If there is not enough space within theprediction horizon to shift the load of a heat pump, the model is not able to find a feasible solution.In these cases the sub-gradient iteration is terminated by a maximum number of iterations.

Given the update of (33), it can be seen that each prosumer i will receive a similar shadow pricesince the update is based on the cumulative total load of the prosumers. The shadow price is namelyassociated with the load of the line connecting the transformer. So, according to the objectivefunction (30), every sub-load through that line will receive the shadow price of the line multipliedwith the amount of load of prosumer i. If 2 prosumers congest a line and would have completely

45

identical characteristics, the shadow price would converge to a price that would ensure that exactlythe two prosumers fill out the capacity of the line. In that case each prosumers is assigned halfof the maximum permissible load of the line. For example, consider the simple case of 3 identicalprosumers sharing a line with a 3 kW capacity constraint. Assuming that all 3 prosumers would loadthe line at the same time with a 1.1 kW heat pump, a cumulative load of 3.3 kW would congest theline. Hypothetically the shadow price would converge to a price that ensures that the capacity ofthe 3 kW line is fairly divided over the three prosumers, that is, each household would receive a 1kW share. However, this 1 kW is not sufficient to cover the 1.1 kW requirement of the heat pumpwhen taking the physical inability of the heat pump to modulate its power input into consideration.A feasible solutions shall not be found. Ideally 1 of the 3 prosumers shifts its flexibility forward orbackward in time away from the original time of congestion. The enabling of only 2 heat pumpswould not cause any congestion. The latter can only be ensured by non-identical prosumers thatwill respond differently to an identical shadow price. Non-identical prosumers in that case refers toprosumers with, for example, different buffer levels, different heat demand patterns, different goalfunctions, etc.

Now that the problem consists out of 2 Lagrange multipliers, 2 sub-gradient iterations are requiredto find a solution. When the sub-gradient method with respect to the first Lagrange multiplier λconverged and the sub-gradient method with respect to the second Lagrange multiplier µ resultedin a non-congested prediction horizon, the first control input f i(τ)|τ=k will be implemented and theprediction horizon is moved forward to find the next control input f i(τ)|τ=k+1. It was mentionedthat whenever our problem is convex, the solution of Algorithm 1 would converge to the solutionof the original problem problem. With the addition of the Lagrange multiplier µ, the algorithm ismodified into Algorithm 2.

Result: Find 4f i(k) at each cycle k of the distributed MPC methodfor k = 0, ..., T do

each prosumer i measures xi(k),wi(k);while

∣∣∣λi,r(τ) – λi,r–1(τ)∣∣∣ > ε and∑i∈z

(f i(τ) + gi(τ)

)≥ Lz,max(τ) do

for i = 1, .., n dosolve (31);

endeach prosumer i communicates {xi(τ)}

k+Kpred

τ=k to connected prosumers;for i = 1, .., n do

sub-gradient update (26);endeach prosumer i communicates {λi(τ)}

k+Kpred

τ=k to connected prosumers;for i = 1, .., n do

sub-gradient update (33);endeach prosumer i receives {µz(τ)}

k+Kpred

τ=kendeach prosumer i implements 4f i(k) = 4f i(τ)|τ=k;

endAlgorithm 2: Adjusted Distributed Model Predictive Control

Even though the capacity constraint might not be violated, the shadow price µ is still updated.When there is no congestion detected in the prediction horizon, µ will be updated with a negativevalue since the term

∑i∈z

(f i(τ) + gi(τ)

)– Lz,max(τ) becomes negative. Both Lagrange multipliers

46

affect each other. If congestion at τ does not occur but the update of λ has not yet converged tothe threshold ε, µr+1(τ) < µr(τ). However, at the next iteration the situation can arise that, withnew information, a temporary solution is found that would cause congestion. Subsequently, µ willincrease to penalise the use of the flexible load. Whereas λ converges towards ε, the transformercan be alternating between congested and non congested, subsequently µ can increase and decreasewithin the while loop from Algorithm 2. The while loop is terminated when both conditions are met,that is, the expected influence of the neighbours reaches the predicted imbalance and the solution isfeasible with respect to the capacity constraint.

The model can be extended to host multiple constraints of different transformers. Each prosumeris only connected to a single transformer. Different prosumers, connected to different transformerswould receive transformer specific shadow prices. Consequently, each transformer would result in anadditional condition to the while loop of 2 and the installment of an additional sub-gradient methodupdating the prices for each transformer individually.

5.3 Day Ahead Planning and goal function

As seen in the flow diagram from Figure 5 in Section 2.5, the DAP acts as the desired trajectory forthe MPC. Pons (2013) used real data on fixed electricity load and heat demand available within DNVGL. In order to create a forecast that would act as the DAP, the known demand is approximated witha moving average. By doing so, a deviation between the DAP and the actual demand is establishedand flexibility is required within the operate phase in order to minimise the gap.

The decoupled objective function that every prosumer can solve on its own requires a goal functionin the dynamic state equation from equation (32) that represents the individual obligation of everyprosumer that accumulates to the DAP. The DAP is thus split up into individual goals for individualprosumers as explained in chapter 4.2.2. Pons (2013) divides the goal function uniformly over theprosumers and thus every prosumers contributes the same to the greater goal of the DAP. Doddema(2014) uses the same principle but divides the DAP over the prosumers according to their meanelectricity demand, thus resulting in a weighted distribution of the DAP among the prosumers.

Since the amount of flexibility a prosumers possesses can be quantified, as described previously inChapter 3 it makes more sense to divide the goal function based on that amount of flexibility. Bydoing so, the prosumer with the most flexibility obtains the biggest part of the DAP. However, thereis no mathematical proof yet, that this specific division will improve the performance of the d-MPC.Nevertheless, it is a more natural reasoning compared to the one used in previous work.

Algorithm 3 is designed to quantify flexibility and divide the DAP. The DAP will be divided during theoptimisation at every time step t in order to include the changing flexibility levels of the prosumersduring the optimisation. If the sum of electricity demand (i.e. fixed electricity demand plus theelectrical equivalent of the heat demand) over prediction horizon τ = [k, k + Kpred] is smaller thanthe sum of the DAP within that same prediction horizon, ramp up flexibility is required to increasethe electrical load and thereby minimise the deviation with the DAP. Vice versa, if demand is biggerthan the DAP, the deviation is minimised by ramping down. In the first case a bigger goal shouldbe given to the prosumer with more ramp up flexibility whereas in the latter case the prosumer withthe most ramp down flexibility should be appointed the biggest goal function.

When ramp up flexibility is required, equation (4) is rewritten to match the setup of the model aspresented before. Every time step k during the simulation, the ramp up flexibility that each prosumer

47

i possesses over the prediction horizon τ = [k, k + Kpred] is defined as:

F+i (k) =

∫ k+Kpred

k

[min

(((1 – δi(τ)) · C(1 –

bufferi(τ)C –

k+Kpred∑k

(dheat,i)

C

)α · t

), Pnom

)](34)

such that flexibility is approximated by the area under the plot as depicted in Figure 12 in orderto quantify the ramp up power that can be sustained within the prediction horizon τ = [k, k +Kpred].

Figure 12: Ramp up flexibility

In this specific example, the buffer is full before the end of the prediction horizon τ = k + Kpred.Other prosumers might not be able to fill the entire buffer within the prediction horizon, whichjustifies integrating over the entire prediction horizon.

Note that the forecasted heat demand over the prediction horizon is subtracted, since the buffer isfilled by α and drains by dheat within the prediction horizon. Subtracting the heat demand thusensures more buffer to be filled up. For reasons of simplicity in modelling it is assumed that thisfreed up space is subtracted from the buffer at time step τ = k at the beginning of the predictionhorizon.

The ramp down flexibility as defined by equation (6) is rewritten to

F–i (k) = max

((–δi(τ) · bufferi(τ)k+Kpred∑

k(dheat,i)

), –Pnom

)(35)

Note that in equation (35) the buffer drains with the actual heat demand of prosumer i, whereasin equation (34) the buffer fills with rate α. Equation (35) thus yields a vector of size Kpred. Atrapezoidal numerical integration over this vector serves as proxy for the ramp down flexibility overthe prediction horizon.

48

In both cases, either a request for ramp up flexibility or for ramp down flexibility, the sum of flexibilityamong the prosumers is summed in order to determine the weighted division of the DAP.

Result: Determine the division of the DAP in goal functions among prosumers.DAP = min(constraint, moving average)for k = 0, ..., T do

if {demand}k+Kpred

τ=k < {DAP}k+Kpred

τ=k thenramp up flexibility is required;for i = 1, ..., n do

solve (34)endfor i = 1, ..., n do

goali(k) =F+i

n∑i=1

F+i

·DAP(k)

endelse if {demand}k+Kpred

τ=k > {DAP}k+Kpred

τ=k thenramp down flexibility is required;for i = 1, ..., n do

solve (35)endfor i = 1, ..., n do

goali(k) =F–i

n∑i=1

F–i

·DAP(k)

endend

Algorithm 3: Goal function allocation algorithm

5.4 USEF interpretation

Zooming in on Figure 11, illustrating the operation phase, yields Figure 13 in order to pinpoint thelink between USEF and the design in which the DSO is embedded as presented in Section 5.2.

Remark 6. That the sequence of flexible appliances in the operate phase, which minimises the offsetwith the DAP from the plan and validation phase, remains free of congestion, is ensured by theLagrange multiplier µ.

Remark 7. When, during the operate phase, unforeseen congestion is detected the addition of thesub-gradient method in which the shadow price µ, that prevents congestion, is sought for reflectsthe interaction between the DSO and the aggregator in Figure 13.

Whenever there is detected congestion that would alter the operation regime from the yellow regimeto the orange regime of graceful degradation, the shadow price µ is increased thereby penalisingturning on the heat pump in order to find a sequence that does not congest the transformer. Theincreasing of µ thus refers to the interaction of place flexibility order and collect flexibility orderbetween the DSO and the aggregator in Figure 13. With the updated µ the algorithm looks fora new solution corresponding to the aggregator re-optimising its portfolio. USEF does not allowfor placing any new flexibility orders in the operate phase given time limitations within this phase.Therefore, only outstanding flexibility offers from the aggregator can be ordered. When the DSOstill detects congestion within the prediction horizon, the same routine of increasing the Lagrange

49

multiplier µ is repeated until all congestion is cleared.

Remark 8. All possible options to shift the load of the flexible appliance within the prediction horizonare regarded as outstanding flexibility offers from the aggregator. The d-MPC algorithm ensures thatthat option is picked which ensures the minimisation of the desired trajectory of the BRP and whichnot results in violating the constraint at the transformer.

Figure 13: DSO involvement in the operate phase of USEF. Copyright USEF Foundation (2015)

Remark 9. The role of the BRP in the operate phase is neglected. The DAP embodies the interestof the BRP. The d-MPC application allows for any alteration upon this DAP by the BRP duringthe operate phase and the optimisation. However, this is neglected in this thesis and the DAP isassumed to be static and known before the start of the operate phase of USEF.

When there is no feasible solution without congestion the algorithm is terminated given a predeter-mined maximum number of iterations in which the problem should be solved if there is a feasiblesolution. If the latter is not the case, congestion is not solved and the orange regime is operational.In this case the aggregator will have to financially settle with the DSO in the settlement phase ofUSEF. It is also in this phase that the aggregator and the BRP settle for the possible offset of theoptimal sequence with the desired trajectory of the DAP. The d-MPC algorithm only reflects thegreen and yellow regime and excludes the orange regime and is thus not able to incorporate gracefuldegradation to ensure the yellow regime is reached once again.

Since the designed d-MPC application solely covers the operate phase of USEF, only the active roleof the DSO within that phase can be modelled. The active role of the DSO in the plan and validationphase of analysing the safety of the grid is included in the definition of the outcome of those phases,the DAP. In Remark 4 in Section 4.3 it is assumed that the DAP is free of congestion. As can be seenin Algorithm 3, this is done via a minimum statement min based on the initial moving average uponwhich the DAP is based. Hereby it is prevented that the orange regime is reached in the validationphase if not enough flexility could be procured and congestion could not be prevented.

In summary, when the system remains in the green or yellow regime, the solution to be found shouldminimise the imbalance with the DAP of the BRP. When congestion is detected the algorithmprevents reaching the orange regime by using the flexibility for congestion management. In thecurrent model the DSO is thus the only party actively ordering outstanding flexibility orders sincethe interest of the BRP is already taken into account via the DAP. Any alteration on the optimalsequence of turning the flexible appliances on and off for congestion management as requested by

50

the DSO is expected to result in a decrease in performance. More elaboration upon the performanceof the algorithm can be found in Section 6.6.

In this chapter, the d-MPC model that includes the active role of the DSO in the operate phaseof USEF is presented. This role is captured by adding an additional Lagrange multiplier and anassociated sub-gradient method that mimics a market mechanism with an economic signal as externaltrigger to shift loads in time. In Chapter 6 model choices, in order to run simulations and test theeffectiveness of congestion management, will be elaborated upon.

51

6 SIMULATION SETUP

In Chapter 4, MPC in general and d-MPC in specific have been presented. In Chapter 5 the DSOhas been added to the d-MPC via an additional shadow price µ. Moreover, it is explained how thisaddition can be interpreted within USEF as presented in Chapter 2.

In order to run simulations with the proposed design of the d-MPC, several model choices have to bedefined. This concerns the information matrix A, the definition of the flexible appliances available,the quantification of the capacity constraint Lmax on the transformer, a switch penalty in order todeal with excessive state switching, the demand patterns used as input for the simulation study andthe definition of the performance indicator in order to be able to quantify the effect of the embeddingof the DSO with respect to the initial model neglecting the DSO. In this chapter, these choices willbe elaborated upon in succession.

The model is written and run within the MATLAB environment of MATLAB R2014a while usingGurobi Optimizer to solve the inner optimisation problem from equation (31).

6.1 Network coupling

The problem presented is a multi-agent system in which every agent solves its own problem. Besidesthat, the agents, or prosumers in the setting at hand, share information with neighbours as definedby an information network. This networks does not have to resemble the actual geographical networkand the corresponding power network (Scherpen, 2015). It is stated in Subsection 4.2.1 that prosumeri is dynamically coupled to his informational neighbour, prosumer j, by a weighting A in order toshare imbalance as defined by the dynamic state equation from equation (32). The informationnetwork is defined as

A =

0.6 0.2 0 0 . . . 0.20.2 0.6 0.2 0 . . . 00 0.2 0.6 0.2 . . . 0...

... . . . . . . . . . ...0 . . . 0 0.2 0.6 0.20.2 . . . . . . 0 0.2 0.6

(36)

Every prosumer has 2 neighbours with which imbalance is shared. The neighbours’ information isweighted 0.2 whereas the prosumer’s own imbalance is weighted 0.6. The information matrix asdefined in (36) meets the requirements as stated in Subsection 4.2.1. The columns add up to 1ensuring that all information is conserved within the system. Moreover, all weights are non-negativeand the information matrix A is strongly connected. The latter implies that information from anyprosumer can get to any other prosumer, as can be seen in Figure 14.

1 2 3 … n 0.2

0.2 0.2 0.2 0.2

0.2 0.2 0.2

0.6 0.6 0.6 0.6 0.6

0.2

0.2

Figure 14: Graph of the information matrix with n prosumers. Information weighted 0.2 is sharedamong neighbours. Information weighted 0.6 concerns the prosumer’s own imbalance.

53

6.2 Flexible appliances

In the original centralised MPC simulation of Pons (2013), 2 flexible appliances are considered. Anenergy producing µ-CHP and an energy consuming heat pump. In the follow-up study of Doddema(2014) on d-MPC only the latter was part of the simulations. Due to the focus on the DSO in thisthesis, solely the heat pump is considered.

The heat pump moves thermal energy from a heat source, the heat sink, opposite to the directionof spontaneous heat flow, from a cold area to a warmer area. The second law of thermodynamicsstates that heat cannot flow from a colder area to a warmer area spontaneously. Therefore, the heatpump requires external power and thus consumes electricity. The term heat pump generally refers toall HVAC devices concerned with heating, ventilating and air conditioning. In this research the focusis solely on the heating application of the heat pump. Different types of heat pumps, like air sourceheat pumps, ground source heat pumps and hybrid heat pumps among others can be consideredwithin a heating application. The functional description of consuming electricity and producing heatto a heat buffer is the one of interest within this study. Therefore, different types of heat pumpsare not considered. Instead, a generic heat pump is available to every prosumer. This heat pump ischaracterised by the following constraints.

• The heat pump cannot modulate in power. Thus, it is either turned off and not consumingelectricity or turned on and consuming nominal power Pn. This behaviour can be capturedin the following constraints via a binary state variable δi(τ) that indicates the state of theappliance.

{P = 0 if δi(τ) = 0

P = Pnom if δi(τ) = 1(37)

The heat pump consumes Pnom = 1.1 kW.

• The heat pump is, once started, operating for at least Ton = 2 time steps. Therefore the modelshould keep track of the time of operation denoted by ton(τ).

ton,i(τ + 1) =

{ton,i(τ) + 1 if δi(τ + 1) = 1

0 if δi(τ + 1) = 0(38)

The Gurobi Optimizer solver requires that constraints are written with the variables to beoptimised on the left hand side of the equation. The previous constraint is thus written asfollows:

ton,i(τ + 1) – tmaxon δi(τ + 1) ≤ 0

ton,i(τ + 1) – ton,i(τ) ≤ 1

ton,i(τ + 1) – ton,i(τ) – tmaxon δi(τ + 1) ≥ 1 – tmax

on

(39)

with tmaxon = 2 acting as an upper bound on ton. Consequently, ensuring that the heat pump

remains operating for at least Ton = 2 time steps is embedded as

Ton · δi(τ) – ton,i(τ) ≤ Ton · δi(τ + 1)

Ton · δi(τ) – ton,i(τ) – Ton · δi(τ + 1) ≤ 0(40)

54

• Likewise, the heat pump is, once stopped, idle for at least Toff = 2 time steps. The time of beingof idle is captured by toff(τ)

toff,i(τ + 1) =

{toff,i(τ) + 1 if δi(τ + 1) = 0

0 if δi(τ + 1) = 1(41)

and rewritten for use within the Gurobi Optimizer environment

toff,i(τ + 1) + tmaxoff δi(τ + 1) ≤ tmax

off .

toff,i(τ + 1) – toff,i(τ) ≤ 1

toff,i(τ + 1) – toff,i(τ) + tmaxoff δi(τ + 1) ≥ 1

(42)

with tmaxoff = 2 acting as an upper bound on toff . And similar to the on timer,

– Toff · δi(τ) – toff,i(τ) ≤ –Toff · δi(τ + 1)

– Toff · δi(τ) – toff,i(τ) + Toff · δi(τ + 1) ≤ 0(43)

• Consistent with the previous models of Pons (2013) and Doddema (2014) the heat pump consumesPnom = 1.1 kW and produces 3.3 kW of thermal power when turned on. This heat istransferred to a heat buffer with a maximum capacity of C = 12.6 MJ. The buffer levelchanges according to

bufferi(τ + 1) = bufferi(τ) + α · f i(τ + 1) – dheat,i(τ + 1) (44)

where α captures the conversion from kW to MJ per time step and dheat,i(τ) resembles theheat demand demand of prosumer i. Thus, the buffer fills up with a rate of α per time stepand drains with the forecasted demand. In Section 3.2, α was calculated as 900kW/kJ or0.9kW/MJ per 5 minute time steps. dheat,i(τ) is given by the demand patterns as will bedescribed in Section 6.5.

Rewritten to the Gurobi Optimizer environment yields

bufferi(τ) – bufferi(τ + 1) + α · f i(τ + 1) = dheat,i(τ + 1) (45)

6.3 Capacity constraint

In order to quantify the capacity constraint Lmax in Algorithm 2, the maximum simultaneous loadon the transformer is of interest. In Section 2.4 the model of Rusck was mentioned to calculate themaximum load of a group of n prosumers based on the simultaneity factor and the maximum load ofa single prosumers. However, this maximum load of a prosumer is not easily determined. Velanderbased his approach to determine the maximum load, or peak load, on the easily obtainable yearlyelectricity consumption V instead (Oirsouw van, 2012):

Pmax = γ ·V + β ·

√V

n(46)

where γ and β are parameters determined by measurements. Typical values are γ = 0.23 · 10–3and β = 0.016 (Oirsouw van, 2012). Given these and annual consumption values, Figure 15 shows

55

the maximum peak load per prosumer relative to the amount of prosumers connected to the samedistribution network.

0

0.5

1

1.5

2

2.5

1 10 100 1000

Pmax [kW]

Number of n connected prosumers

V=4300 kWh/year V=3500 kWh/year

Figure 15: Maximum simultaneous peak load of n prosumers based on annual energy consumption

With the maximum peak load per connection as shown in Figure 15, the maximum simultaneouspeak load over a network is, so to speak, divided over the prosumers connected within that network(Oirsouw van, 2012). An increase in the number of prosumers thus decreases the maximum peakload that occurs at the transformer. These numbers correspond with the values as mentioned bythe professionals2 which speak of values ranging from 1.1 kW to 1.4 kW as maximum simultaneouspeak load. When presenting the simulations in Chapter 8, the effect of the constraint is elaboratedupon.

For years, Velander and rules of thumbs, based on experiences, were used to design distributiongrids. However, Velander’s method is criticised and deemed obsolete. Hemmingsson and Lexholm(2013) conclude that the shortcomings of the model of Velander, the fact that the time at whichthe maximum load occurs is not considered and that the model is only suitable on networks con-sisting of similar types of prosumers with respect to energy consumption and patterns, result in anoverestimation of peak loads. You et al. (2014) states the importance of improving distributionnetwork planning and design tools in order to better incorporate emerging technologies associatedwith increasing shares of distributed generation, electricity storage and foremost smart grid productson measurement, communication and control.

Nevertheless, in this thesis the focus lies upon the current state of affairs, that is, the existingelectricity infrastructure. This infrastructure is already installed and it is in these networks whereflexibility can play an important role by decreasing the peak load through demand shifting in orderto prevent capital intensive reinforcements of the network. In the design of distribution networksthat yet have to be build, a new residential area for example, the previous mentioned trends will beincorporated to improve the outdated approach of Velander. It is in the best interest of the DSOto safeguard security of supply at the minimum amount of costs. As noted by Hemmingsson andLexholm (2013), it is a common understanding that the marginal costs for a thicker cable, thatreduces the need for peak reduction, is a small fraction of the cost related to the construction of adistribution network. In that case, there is no use of flexibility to prevent congestion. However, inexisting networks, procuring flexibility presents itself as a cheaper or even the only feasible solutionin order to prevent congestion. Updating cables in the old city centre of Amsterdam, for example, iscostly and undesirable. Given the aim of using flexibility to prevent congestion in given distributionnetworks, the specifications of such an network, partly based on outdated models like Velander andacknowleged by the interviewed professionals, should be considered.

2Milo Broekmans from Stedin and Marcel Bogaerts from Alliander. Both Stedin and Alliander are DSOs.

56

6.4 Excessive state switching

The model presented before is a Mixed Integer Quadratic Programming (MIQP) problem given thequadratic objective function in equation (30) and the binary state variable δ in equation (37). Theheat pump can only be turned on or off and thus cannot take any value in the continuous interval [0, 1].Unfortunately, finding a solution is therefore not guaranteed. Larsen (2014) clarifies that excessivestate switching, an oscillation between turning on (or off) and staying off (or on) is expected. Asolution is to consider the ability of the heat pump to modulate power but results in solutions thatmight not be implemented in practice. A MIQP can be more time consuming to solve but resultsin implementable solutions. However, the introduction of the binary state of the heat pump makesthe problem non-convex a solution harder to find and oscillations might occur. Larsen (2014) stopsthe sub-gradient optimisation whenever oscillation is detected and implement the last state beforethe oscillations started. Doddema (2014) used a different approach and embedded a switch penaltyin the prosumers individual optimisation problem. The penalty is made a function of the iterationnumber, resulting in freedom for the device to switch in the early stages of the sub-gradient iterationswhile increasingly penalising excessive state switching in the long term. This approach resulted ina significant decrease in the number of iterations necessary to obtain convergence. The excessivestate switching penalty as presented by Doddema (2014) remains untouched in this thesis given thesuccessfulness of the approach.

6.5 Demand patterns

The demand patterns concerning fixed electricity demand and heat demand are similar to the onesas used by Doddema (2014). Thereby, results are easily compared among the initial model and theextended model as presented here. The datasets contain data on electricity and space heating fortwo days and 250 households with an one minute time resolution, representing two days at the end ofNovember in the Netherlands. A substantial amount of heat demand is therefore available resultingin sufficient opportunities to analyze the flexibility of the heat pump and buffer combination.

Figures 16 and 17 show the demand patterns for electricity and heat respectively for the 250 house-holds. Both patterns show morning and evening peaks in both days.

0

50

100

150

200

250

0 8 16 24 32 40 48

Electricity

dem

and [kW]

Time [hours]

Figure 16: Electricity demand pattern [kW] for 48 hours and 250 households.

57

0

10

20

30

40

50

60

70

0 8 16 24 32 40 48

Heat dem

and [M

J]

Time [hours]

Figure 17: Heat demand pattern [MJ] for 48 hours and 250 households.

6.6 Performance indicator

Simulations in Chapter 8 are analysed on the ability of the algorithm to prevent congestion and tominimise imbalance. The first will be verified by plotting the total load on the transformer and theconstraint of that transformer versus time. The latter will be checked by summing over the numberof prosumers and over the time steps k=[0,T] of the individual objective function as defined byequation (16) yielding

V(k) =T∑

k=1

( n∑i=1

(|xi(k)|2Qi

+ |4f i(k)|2Ri

))(47)

It is expected that when the DSO requires flexibility to prevent congestion, the overall performance ofthe model will be lower (i.e. V in equation (47) will become larger) since the optimal sequence of theoperation of flexible appliances that minimises equation (47) is altered to prevent congestion.

In the setting of USEF, the BRP desires to minimise the total physical imbalancen∑

i=1

xi(k), the

difference in supply (i.e. the DAP) and demand (the total sum of fixed and flexible load of theprosumers). The DSO overrules the interest of the BRP in order to ensure a safe and well functioningnetwork without congestion.

However, the definition of the performance indicator of equation (47) does not fully reflect theimbalance between the total load of the prosumers and the DAP. First, equation (47) incorporatesthe change in control input, 4f, that is of no interest for the BRP with respect to the total load.Furthermore, even though, as explained in Subsection 4.2.1

n∑i=1

xi(k) =n∑

i=1

xi(k) ∀k ≥ 0.

,n∑

i=1

x2i (k) 6=n∑

i=1

x2i (k) ∀k ≥ 0.

That is, the sum of information imbalance xi(k) equals the sum of physical imbalance xi(k), but thesquare of the sum of information imbalance xi(k) does not equal the square of the sum of physicalimbalance xi(k). Even if Ri = 0 ∀i, the objective function, represented by the performance indicator

58

from (47) that is minimised, is not an adequate representation of the performance of the BRP that

is interested in minimising the physical imbalancen∑

i=1

xi(k).

Pons (2013) defines the performance indicator with respect to minimising physical imbalance xas

xtot =T∑

k=1

( n∑i=1

xi(k)

)2

However, this is not what the model minimises. Therefore there is no guarantee that if equation(47) is minimised, the performance of the BRP as defined by Pons is minimised as well. Besides,Sahriatzadeh et al. (2012) argues that a quadratic cost function is not suited for the electricitymarket since it does not cognitively match how the BRP wants to trade in real life and proposes anon-differentiable piecewise cost function based on real prices. In the current setting, real prices arenot considered making such an approach impossible. The quadratic cost function from Pons (2013)does however ensure that negative and positive physical imbalances xi(k) in different time steps k ofthe simulation do not offset each other. Moreover, it penalises bigger imbalances more then smallerimbalances.

There is a discrepancy between the objective of the d-MPC to minimise the objective function,represented by the performance indicator from (47), and the interest of the BRP to minimise the

total physical imbalancen∑

i=1

xi(k).

Regardless that discrepancy, equation (47) is used to indicate the performance of the model. This isbecause the interest lies merely upon solving congestion in the given model. The expected decreasein performance of the model due to overruling by the DSO in order to prevent congestion is of interestin this thesis.

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7 SCENARIOS

In order to test the d-MPC with the additional Lagrange multiplier on the ability to resolve congestion,a multitude of scenarios can be defined. In each of these scenarios the desirable result is the sequenceof turning on and turning off heat pumps in order to meet a given heat demand and to follow thepredetermined path of the DAP as close as possible in order to minimise the imbalance of the BRP,while respecting the capacity constraint as formulated by the DSO.

This capacity constraint refers to the capacity limits of a transformer connecting a group of prosumerson the low voltage network with the medium voltage network.

7.1 Topology

Combining the actors within USEF and the physical electricity network results in the topology aspresented in Figure 18. This topology represent both the informational network and the physicalnetwork. The informational network consists out of the aggregator shifting flexible appliances fromprosumers in time, to reach the desired trajectory of the DAP from the BRP based upon solving 31and the coupling of prosumers as described in Section 6.1.

The physical network consist out of the prosumers who are physically connected via power lines tothe Low Voltage (LV) transformer that connects the LV network with the Medium Voltage (MV)network. Both networks unite at the prosumer. The sequence of turning the heat pumps of theprosumers on and off results in physical loads at the transformer. It is thus at these prosumers wherethe informational network and the physical network unite.

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Figure 18: Network topology with a single aggregator. Combining the informational network andthe physical electricity network.

The USEF interaction model depicted in Figure 1 describes the relation between the different actorswithin USEF. The relationship between the BRP and aggregators is of N-to-M, meaning that N ∈ NBRPs will interact with M ∈ N aggregators given the relation as described by USEF. The relationshipbetween the aggregator and the prosumers is described via the aggregator and the ADS owned by theprosumer. For reasons of simplicity that is regarded as a direct relation between the aggregator and

61

the prosumer. This relationship is characterised by USEF as 1-to-K. A single aggregator controlsthe ADS of K ∈ N prosumers. However, the ADS of a single prosumer can only be controlled by1 aggregator. In Section 4.3 it was stated that Pons (2013) and Doddema (2014) restricted theirapplication to a single BRP in order to neglect the imbalance market where electricity is tradedamong BRPs. This all gives rise to a variety of scenarios hosting a single BRP, multiple aggregatorsand multiple prosumers. Prosumers that are physical neighbours and thus share a connection atthe same LV transformer do not have to be controlled by the same aggregator and therefore do nothave to be informational neighbours that are connected via the information matrix A as defined inSection 6.1. Likewise, informational neighbours controlled by the same aggregator do not have tobe physical neighbours sharing a connection to the LV transformer. Such a topology is depicted inFigure 19.

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Figure 19: Network topology with multiple aggregators. Combining the informational network andthe physical electricity network.

Besides a single BRP, the d-MPC algorithm of Doddema (2014) hosts a single aggregator. Thereforeit is a logical scenario for the extended d-MPC algorithm to consider a single BRP, a single aggregator,a single LV transformer and multiple prosumers connected to that LV transformer. Such a scenarioyields a topology as depicted in Figure 18. By altering the demand of these prosumers, congestionon the transformer connecting the MV and the LV network is ought to be prevented.

62

8 SIMULATIONS

The d-MPC method, fitted to the operation phase of USEF and designed to prevent congestion, aselaborated upon in Chapters 5 and 6 is tested upon several simulations to proof its ability to do so. Inthis chapter, several simulations will show the performance of the model. Firstly, different methodsof dividing the DAP into a prosumer individual goal function as mentioned in Section 5.3 will beelabrated upon. Thereafter, in Section 8.2, the ability to prevent congestion will be reviewed.

8.1 Quantification of flexibility to divide the Day Ahead Planning

In Section 5.3 an algorithm was proposed that, based on the quantification of flexibility as discussedin Chapter 3, divided the DAP among the prosumers. It was noted that there was no evidencethat this division would perform better than the division based on the mean electricity demand asproposed by Doddema (2014). The base simulation consists out of 3 prosumers within a time horizonof 12 hours with 15 minute time steps. The DAP is determined via a moving average of the demandpattern. These patterns and the resulting DAP are depicted in Figure 20. The blue bars represent theelectricity demand in kilowatt of 3 prosumers per 15-minute time steps. The yellow bars representthe electrical equivalent of the heat demand in kilowatt, again per 15-minute time steps. The blackline depicts the DAP and represents the amount of kilowatts bought by the BRP.

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time step

De

ma

nd

[kW

]

Total Elektricity and Heat Demand

Electricity Demand Heat Demand Day Ahead Planning

Figure 20: Electricity and heat demand for 3 prosumers for 12 hours (48 15-minute time steps).

Three different methods of dividing the DAP intro prosumer specific goal functions are considered.The equal division among prosumers from Pons (2013) can be seen in Figure 21, whereas the weighteddivision based on consumption from Doddema (2014) is illustrated in Figure 22. Finally, the divisionbased on the quantification of flexibility as proposed in Section 5.3 is depicted in Figure 23. All threefigures show, per 15-minute time steps, the same DAP. The red, green and orange bar depict thegoal functions of prosumer 1, 2 and 3 respectively per 15-minute time steps. Obviously, the sum ofthe individual goal functions equals the DAP at every time step t.

63

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4

Day Ahead Planning and Goald Function

Time step

Go

al [k

W]

Figure 21: Equal division of the Day Ahead Planning among the prosumers.

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4


Time step

Go

al [k

W]

Figure 22: Weighted division of the Day Ahead Planning among the prosumers based on demand.

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4


Time step

Go

al [k

W]

Figure 23: Weighted division of the Day Ahead Planning among the prosumers based onquantification of flexibility.

The differences among these divisions are clearly visible. Since prosumer 1 is the biggest consumer,it receives the biggest goal function as can be seen in Figure 22. In the methods of Pons (2013) andDoddema (2014) the DAP and the individual goal functions of the prosumers are determined beforethe actual for loop in Algorithm 1 hosting the actual optimisation. The method of division based onthe quantification of flexibility is dynamic and thus updated during the optimisation based on actualcontrol inputs and buffer levels. That results in instances for which the entire DAP is assigned as agoal function to a single prosumer. For instance, in time step 40, as can be seen in Figure 23, thegoal function of prosumer 2 equals the DAP. At time step 40 the fixed electricity demand plus theelectrical equivalent of the heat demand over the prediction horizon is bigger than the DAP within

64

that same prediction horizon. Subsequently, ramp down flexibility is required in order to get closerto the DAP. As explained in Chapter 3, ramp down flexibility can only be obtained by shutting arunning heat pump down. It turns out that at time step 40, only the heat pump of prosumer 2 isengaged and is thereby the only heat pump that possesses ramp down flexibility. Likewise, at timestep 36, ramp up flexibility is required. Prosumer 3 turns out to be the only prosumer possessingramp up flexibility and therefore receives the entire DAP as goal function.

With respect to the overall results, based on the performance indicator from equation (47), theequal division of the DAP yields the best performance within this simulation setup with V = 13.29kW2, followed by the weighted division on electricity demand with V = 13.68 kW2. The proposedweighted division on the quantification of flexibility performs the worst with V = 15.36 kW2.

The difference in performance between the equal division and the division based on flexibility can beseen in the solutions as given by the d-MPC. In Figure 24 the optimal sequence of control inputsthat minimises equation (47) is graphically represented in the case of fairly dividing the DAP amongthe prosumers. In the remainder of this thesis this is the chosen visualisation blueprint of the resultsof the d-MPC algorithm. The blue bars represent the sum of fixed, non-flexible, electrical load of the

three prosumers, or3∑

i=1gi(k), in kilowatts per 15-minute time step. The red, green and orange bars

represent the flexible load, or the energy consumption of the heat pumps of respectively prosumer1, 2 and 3. Thus red represents f1(k), green represents f2(k) and orange represents f3(k), all inkilowatts and per 15-minute time steps.

0 5 10 15 20 25 30 35 40 450

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3

4

5

Time step

Lo

ad

[kW

]

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Fixed load Flexible Load 1 Flexible Load 2 Flexible Load 3 Day Ahead Planning

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2

4

6

8

10

12

Time step

Le

ve

l [M

J]

Buffer Levels

Household 1 Household 2 Household 3

Figure 24: Results while dividing the Day Ahead Planning fairly among the 3 prosumers.V = 13.29 kW2.

In Figure 25, the result is depicted while dividing the DAP based on the quantification of flexibil-ity.

65

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

Time step

Lo

ad

[kW

]


Fixed load Flexible Load 1 Flexible Load 2 Flexible Load 3 Day Ahead Planning

0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

Time step

Le

ve

l [M

J]

Buffer Levels


Figure 25: Results while dividing the Day Ahead Planning among the 3 prosumers based on thequantification of flexibility. V = 15.39 kW2.

Three differences can be distinguished between the two solutions. The heat pump of prosumer 3 isturned on later in Figure 25 (time step 8) compared to Figure 24 (time step 4). In between time steps35 and 39, the heat pump of prosumer 2 is turned on earlier and one time step less when dividingthe DAP based on flexibility. At the last time step, time step 48, the heat pump of prosumer 2 isnot turned on in Figure 25 where it is turned on in Figure 24. These three differences reflect thatdividing the DAP based on the quantification of flexibility decreases the performance with 15.8%compared to fairly dividing the DAP for this specific example.

Due to the more natural way of dividing the DAP based on the availability of flexibility, as explainedin Section 5.3, the presumption that it will yield better performance of the application prevails.However, given the current lack of mathematical proof and the absence of clear indications fromthe previous example, the weighted division of the DAP based on the electricity consumption asproposed by Doddema (2014) will be used in the remainder of this thesis. This in order to beconsistent with the work of Doddema and to analyse, ceteris paribus, Algorithm 2 on the ability toprevent congestion. The quantification of flexibility and the proposed method of dividing the DAPbased upon this quantification provides plenty leads for future research.

8.2 Congestion Management

In order to analyse the working of Algorithm 2 from Section 5.2 to prevent congestion, multiplesimulations will be reviewed. The simulations will start off with a small amount of prosumers and asmall simulation period, making it easier to comprehend how the model performs. 3 prosumers, atime horizon of 12 hours in 15 minute time steps and a prediction horizon of 2 hours or 8 time stepsis considered in Subsection 8.2.1.

8.2.1 Simulation 1, 3 prosumers on a 12 hour time horizon

In Figure 26 the fixed electricity and heat demand of 3 prosumers, that are randomly picked out ofthe available pool of 250 households, is shown. The heat demand is represented by the electricalequivalent of that heat demand given the heat characteristics of the heat pump modelled. Both theelectricity and heat demand are given in kilowatts per 15-minute time steps. Moreover, the DAP,based on the summation of both the electrical demand and heat demand is shown as well is thecapacity constraint on the transformer connecting the 3 prosumers to the medium voltage electricitynetwork. The latter is set to 3.3 kW given a yearly consumption of 3500 kWh per prosumer. It canbe seen that providing the necessary heat demand with electricity, rather than with gas, results in asubstantial increase in total electricity demand. As a result, only based on the total demand, there

66

are already 2 time steps at which congestion can be foreseen, namely at time step 43 and 44. Note,however, that the DAP as output of the plan and validation phase is free of congestion as describedin Remark 4 in Section 4.3

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time step

De

ma

nd

[kW

]



Figure 26: Simulation 1. Electricity and heat demand for 3 prosumers for 12 hours (48 15-minutetime steps).

Figure 27 shows the result of the model when the constraint is neglected. In the upper graph,the blue bars represent the fixed electrical load and the red, green and orange bars represent theenergy consumption of the heat pumps of respectively prosumer 1, 2 and 3. In the lower graph inFigure 27 the resulting buffers levels of the three prosumers are depicted. Initial buffer levels arerandomised. Figure 27 shows the optimal sequence of control inputs, the three heat pumps, thatminimises equation (47).

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

Time step

Load [kW

]


Fixed load Flexible Load 1 Flexible Load 2 Flexible Load 3 Constraint Day Ahead Planning

0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

Time step

Level [M

J]

Buffer Levels


Figure 27: Simulation 1 without congestion management.

At time step 2 and 3, the heat pump of prosumer 3 is turned on since the buffer of the respectiveprosumer would otherwise drain. Constraints on the buffer levels and the heat pump; the heat pump

67

is turned on when the buffer is empty and when the heat pump is turned on it has to remain operatingfor at least 2 time steps, result in the first major deviation between the total load and the DAP. Asexpected, the increase in heat demand at the second half of the simulation period, as could be seenin Figure 26, results in a substantial use of the heat pump in the second half of the simulation periodas can be seen in Figure 27. This results in congestion at time step 44. Congestion is preventedby implementing a Lagrange multiplier according to Algorithm 2 and results are depicted in Figure28.

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

Time step

Load [kW

]



0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

Time step

Level [M

J]

Buffer Levels


Figure 28: Simulation 1 with congestion management.

The flexible load of prosumer 1 in time steps 42, 43 and 44 is removed. In order to facilitatethis alteration, the heat pump of prosumer 1 is enabled for one extra time step before the initialcongestion. In Figure 27, the heat pump of prosumer 1 operates for 7 time steps between time step33 and 39, whereas in Figure 28, the heat pump is operating for 8 time steps starting from timestep 32. This additional time step of operation ensures that the heat buffer is fuller in time step 39:from 8.5 MJ in Figure 27 to 11.5 MJ in Figure 28. This is enough to meet the upcoming demandfor the next 5 time steps up to time step 46. Thereby the heat pump does not have to be turnedon and congestion is prevented. It can be seen that in Figure 28, prosumer 1 makes more use of themaximum storage capacity of the heat buffer, by draining the buffer with 10 MJ between time step39 and time step 44.

In Section 5.2 it was stated that congestion can only be solved within the prediction horizon. Thatmeans that either a load is deleted, like in the previous example, or the load is shifted to anothertime step within the prediction horizon. In simulation 1, the prediction horizon equals 8 time stepsor 2 hours. The initial congestion was detected at time step 44. 8 time steps earlier, at time step37, the congestion is spotted as can be seen by the shadow price µ depicted in Figure 29.

68

0 10 20 30 40 50 60 70 80 90 100 1100

0.5

1

1.5

2

2.5

Number of iteration

Sh

ad

ow

price

µ

Figure 29: Simulation 1. Shadow price µ at time step 37 per sub-gradient iteration step.

The shadow price is initially updated to a value of approximately 0.94 after the first iteration sincethe congestion at time step 44 is detected. This value is not large enough to discourage congestionand µ is increased to approximately 1.89. This value ensures that at the next iteration, the modelyields a solution that does not cause congestion. However, the update of the shadow price λ isnot yet converged to the threshold ε and the shadow price µ is updated with a negative update,causing µ to decrease to approximately 0.94 again within the next 6 iterations. The shadow priceµ keeps oscillating between updating positively when congestion is detected within the predictionhorizon and updating negatively when there is no congestion detected until λ is converged and µensures that all congestion in the prediction horizon is prevented. At time step 37, it takes 100iterations before both shadow prices ensure convergence and prevention of congestion. Even thoughthe initial congestion at time step 44 is only first detected at time step 37, at time step 32 the resultsfrom the d-MPC model with congestion management already differ from the d-MPC model withoutcongestion management. This has to do with the fact that the shadow price µ keeps updatingduring the sub-gradient iteration that converges the update of the shadow price λ to the threshold ε.Although initially there is no congestion in the prediction horizon at time step 32, running from timestep 32 up to and including time step 39, congestion might occur during the sub-gradient iteration.Subsequently, the shadow price µ is updated and the model yields different results.

Besides prosumer 1, the other prosumers do not have to alter the usage of their heat pump. Anydifferences between the simulation without and with congestion management with respect to theinformational imbalance results from the alteration of the usage of the heat pump of prosumer 1,and thus a change in informational imbalance of prosumer 1 and the sharing of this informationalimbalance among the 2 other prosumers. Figure 30 shows the comparison between the summed

informational imbalance,3∑

i=1xi(k) of simulation 1 without congestion management (i.e. no DSO

plotted in blue) and with congestion management (i.e. DSO plotted in red) in kilowatts per 15-minute time step (k). Recall from Section 4.2.1 and equation (18) that the sum of informationalimbalance equals the total physical imbalance x of the three prosumers.

Regarding Figure 30, negative imbalance refers to the situation in which the total load of the threeprosumers is smaller than the DAP and thus the prosumers consume too little. A positive imbalancerefers to overconsumption, where the total load exceeds the DAP. The operation of the heat pumpof prosumer 1 in time steps 2 and 3 results in a total load that exceeds the DAP as can be seen inboth Figures 27 and 28. As a result, the positive total imbalance in time steps 2 and 3 is clearlyvisible in Figure 30.

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0 5 10 15 20 25 30 35 40 45−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Time step

Ph

ysic

al Im

ba

lan

ce

[kW

]

Imbalance no DSO Imbalance DSO

Figure 30: Simulation 1. Comparison on the physical imbalance on the transformer.

Concerning the prevention of the initial congestion, 2 alterations are visible as mentioned. Prosumer1 enables the heat pump an additional time step at time step 32, thereby increasing the individualand total imbalance from –1.08 kW to 0.02 kW. This provides enough buffer to cover the heatdemand of time steps 42, 43 and 44. As a result, the heat pump can remain idle and the totalimbalance in these time steps drop from 0.28 kW, 0.26 kW and 1.7 kW to –0.81 kW, –0.48 kWand 0.61 kW respectively. The total imbalance over the three time steps, time step 42, 43 and 44,drops from 2.62 kW to –0.68 kW. Thus, the three prosumers as collective alter from consumingtoo much and causing congestion to consuming too little without causing congestion.

The overall effect of congestion management can be captured by the performance indicator as definedby equation (47). The performance V equals 13.79 kW2 for the simulation without congestionmanagement and 14.74 kW2 as a result of congestion management. This is expected. The initialsimulation that causes congestion is the optimal solution with respect to minimising equation (47).Any alteration to the optimal sequence will thus result in a suboptimal solution and worse performance(i.e. a higher value of performance). The cumulative performance with respect to the individualimbalance is shown in Figure 31. This performance is given per 15-minute time step in [kW2], directlyfollowing from the definition of the performance indicator in equation (47). As mentioned, from timestep 32 onwards, differences between the results as depicted in Figures 27 and 28 are visible. Theeffect of these deviations can be seen in Figure 31. Finally, the d-MPC with congestion managementperforms worse with a higher value on the performance indicator over the time horizon.

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Figure 31: Simulation 1, cumulative total individual imbalance performance.

A good check in order to verify that, indeed, the d-MPC model without congestion managementperforms better than the d-MPC model with congestion management, is to run the same simulation1, but only for 44 time steps. From Figure 31 it can be seen that, within a simulation horizon of48 time steps, at time step 44, the model with congestion management performs better than themodel without. However, the model is designed such that equation (47) is minimised over the entiresimulation period. It is thus expected that, when the model is simulated over only 44 time stepsthe d-MPC model without congestion management, again, performs better than the d-MPC modelwith congestion management. Results are shown in Figure 32. Indeed, the d-MPC model withoutcongestion management performs better with V = 14.37 kW2 compared to V = 14.57 kW2 whenthe congestion is prevented.

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Figure 32: Simulation 1, cumulative total individual imbalance performance.

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8.2.2 Simulation 2, 3 prosumers on a 24 hour time horizon

It has been shown that congestion can by prevented by altering the flexible loads of the prosumers.Simulation 1 only showed 1 time step of congestion. In order to check whether the model is able toprevent congestion at multiple time steps, simulation 2 consists out of the same 3 prosumers on a24 hour time horizon (96 time steps of 15 minutes). Figure 33 shows the demand patterns of thethree prosumers. A multitude of instances of congestion can be foreseen. Moreover, note that theDAP is maxed out to the constraint in order to prevent a transition to the orange regime in the planand validation phase of USEF as explained in Section 5.4.

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Figure 33: Simulation 2. Electricity and heat demand for 3 prosumers for 24 hours (96 15-minutetime steps).

Figure 34 shows the result of the d-MPC model without congestion management and reveals 16time steps characterised by congestion. Congestion is ought to be prevented by the d-MPC withcongestion management. Results are shown in Figures 35, 36 and 37.

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Figure 34: Simulation 2. No congestion management and a prediction horizon of 2 hours (815-minute time steps).V = 42.67 kW2 and 16 time steps are congested.

In Figure 35, a 2 hour prediction horizon is able to bring the instances of congestion back to 13. Themodel is not able to prevent all congestion. This is because of a variety of reasons. First of all, theprediction horizon is not big enough to shift all loads causing congestion. Besides, the constraintson the operation of heat pumps prevents the shift ability of loads to the possible time steps withinthe prediction horizon. For instance, in Figure 35, the first congestion that could not have beenprevented occurs at time step 66. This congestion is first detected at time step 59 and from Figure35 it seems that there are 2 possible locations to shift the load of prosumer 3 to without violatingthe constraint, namely time step 58 and 59. However, when the heat pump is turned on it has to be

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turned on for a minimum of 2 time steps and when turned off it has to remain idle for a minimumof 2 time steps. Therefore, the single flexible load of prosumer 3 cannot be shifted in time withinthe prediction horizon, nor can it be deleted due to a heat demand that has to be fulfilled. Theconstraints ensure that a solution without congestion cannot be found.

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Figure 35: Simulation 2. Congestion management and a prediction horizon of 2 hours (8 15-minutetime steps). V = 56.14 kW2 and 13 time steps are congested.

Increasing the prediction horizon, thereby increasing the computing time significantly, should providemore options for the loads to be shifted to while not violating the constraints on the heat pump.Increasing the prediction horizon to 16 and 24 time steps respectively, indeed, yields solutions withless instances of congestion. Figure 36 depicts the results with a 16 time step horizon and therebythe model is able to prevent an additional instance of congestion. Further increasing the predictionhorizon to 24 time steps, of which the results are depicted in Figure 37, brings down the number ofcongestion back to 10 instances.

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Figure 36: Simulation 2. Congestion management and a prediction horizon of 4 hours (1615-minute time steps). V = 48.70 kW2 and 12 time steps are congested.

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Figure 37: Simulation 2. Congestion management and a prediction horizon of 6 hours (2415-minute time steps). V = 53.50 kW2 and 10 time steps are congested.

When analysing the heat demand from Figure 33 and the results shown in Figures 35, 36 and 37it is obvious that the heat demand primarily causes congestion in the second half of the simulationhorizon. Spreading out the peak in heat demand over the simulation period would ensure that flexibleloads are more evenly spread. By increasing the prediction horizon this could be forced. However,in order to relax the load in the second half of the simulation horizon and moving more load intothe first half of that horizon, the prediction horizon should be at least half the length of the totalsimulation period. Subsequently, computing time would increase substantially. Besides, the shadowprices only discourage the use of loads at the time steps of congestion rather than encourage the useof flexible loads at time steps without congestion. Another way to give an incentive to move loadsforwards in time is to alter the DAP. The DAP follows the heat demand closely and the model steersthe state x to this desired trajectory. Therefore the DAP forces the use of heat pumps in the secondhalf of the simulation horizon rather then in the beginning of that horizon. As stated in Section 2.3,the plan phase of USEF is characterised by the interaction between the BRP and the aggregator inorder to find an economically optimised program to supply the demand of energy. The DAP, thatacts as the result of that plan and validation phase as explained in Section 5.4 may thus be subjectedto changes. The d-MPC model illustrated here represent the operate phase of USEF and is clearlyseparated from the plan and validation phase that are ended by a gate closure. Altering the DAP isthus not possible during the operate phase. However, it shows the impact of the DAP on the abilityof the d-MPC to find a non congested solution and gives rise to simulation 3.

8.2.3 Simulation 3. Adjusted Day Ahead Planning.

A DAP that gives an incentive in the beginning of the horizon to prevent congestion in the secondhalf of the horizon can be one as presented in Figure 38. The first half of the simulation horizon ischaracterised by little heat demand. Therefore, buffer levels are initialised to 0 in order to be able tofill up the buffers in the beginning of the simulation horizon.

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Figure 38: Simulation 3. Electricity and heat demand for 3 prosumers for 24 hours (96 15-minutetime steps) with an adjusted Day Ahead Planning.

The result of the d-MPC model without congestion management is shown in Figure 39. The d-MPCmodel with congestion management yields results that are depicted in Figure 40. In Figure 39 it canbe seen that the DAP ensures that the empty buffers are immediately filled, even causing congestionat time steps 1 and 2. Since the heat demand is low in the first half of the simulation period and thebuffers are already full, the next time steps cannot be efficiently used to turn on more heat pumps inorder to prevent congestion in the second half of the simulation horizon. The effect of the adjustedDAP on the amount of instances of congestion in the second half of the simulation horizon is thusminimal compared to Figure 34, 14 instances to 16 instances respectively.

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Figure 39: Simulation 3 without congestion management and a prediction horizon of 6 hours (2415-minute time steps).

Enabling congestion management via the Lagrange multiplier µ brings the instances of congestiondown to 10 as can be seen in Figure 40. Even though the effect of the DAP in order to moveflexible load forward is visible it is uncontrollable and ineffective to act as means of congestionmanagement.

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Figure 40: Simulation 3 with congestion management and a prediction horizon of 6 hours (2415-minute time steps).

8.2.4 Simulation 4, 3 prosumers on a 24 hour time horizon. Relaxed constraint.

In the previous simulations, the capacity constraint on the transformer was based upon a maximumpeak load per connection of 1.1 kW. As discussed in Section 6.3, typical values are ranging from 1.1kW to 1.4 kW. The previously considered constraint was thus a tight constraint. When taking avalue of 1.4 kW as the maximum peak load per connection, the capacity constraint on the transformeris 4.2 kW rather then 3.3 kW and results are shown in Figures 41 and 42 for the d-MPC modelwithout and with congestion management respectively.

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Figure 41: Simulation 4 without congestion management and a prediction horizon of 6 hours (2415-minute time steps).

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Figure 42: Simulation 4 with congestion management and a prediction horizon of 6 hours (2415-minute time steps).

As before, the model without congestion management performs better with V = 38.43 kW2 com-pared to V = 43.85 kW2 for the model with congestion management. However, 3 instances ofcongestion are prevented.

In this chapter the working of the d-MPC model is illustrated and specifically the use of the Lagrangemultiplier µ as means of congestion management is analysed. Moreover, an overview of the differentstrategies to divide the DAP into prosumer specific goal functions is given. Finally the effect of thisDAP on the result of the d-MPC model is shortly elaborated upon. This thesis will be evaluated inChapter 9 were conclusions are drawn and shortcomings and limitations as well as future researchopportunities are discussed.

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9 CONCLUSION

In previous work of Larsen (2014) it is shown that d-MPC is suitable to apply within smart grids.The work of Pons (2013) and Doddema (2014) resulted in a d-MPC application that can be usedas an internal optimisation tool in order to balance power in a network of prosumers within theoperate phase of the MCM of USEF. This d-MPC application is bounded to the green and yellowregime establishing the free market and acting as the modus operandi in USEF. However, the appli-cation neglected the role of the DSO. The role of the DSO is to minimise grid capacity costs whilesimultaneously safeguarding security of supply. Specifically, within the green and yellow regime ofthe operate phase of USEF this entails procuring flexibility from the aggregator in order to preventcongestion.

This thesis contributes to the development of the d-MPC application applicable in USEF by em-bedding the role of the DSO by adding a market mechanism to resolve congestion in the operatephase. In this market mechanism, the Lagrange multiplier µ, acting as economic signal is added tothe decentralised objective function. Thereby the research question as derived at the start of thisthesis is answered.

• How can the role of the DSO be embedded in the given d-MPC application in USEFs MCM?

The extended d-MPC application ensures that each prosumer can individually solve a decentralisedobjective function while the aim is to reach a global goal in the network. This global goal refers theminimisation of imbalance and the prevention of unforeseen congestion at the low voltage transformerconnecting the prosumers to the mid voltage electricity grid. Based on local information and aLagrange multiplier µ relating the total load on the transformer to the maximum capacity, the d-MPC application is able to prevent congestion through the shifting of flexible loads in time. Theseloads relate to the electricity consumption of a heat pump that, in combination with a heat buffer,contains flexibility.

In a simulation setup with realistic data on heat demand and electricity consumption, the workingof the proposed extended d-MPC application is analysed. From these simulation the followingconclusions with respect to the addition of the role of the DSO can be drawn.

• The observed trends on both the demand and supply side of the electricity network ensurehigher simultaneity factors. The resulting increasing stress on the transformers in the lowvoltage distribution grid presents one of the biggest challenges for the DSO to cope with inthe transition to future smart grids. (Chapter 2)

• The active role of the DSO as congestion manager within the green and yellow regime of theMCM in USEF in order to prevent a transition to the orange regime can be translated into theLagrange multiplier µ and the algorithm presented suitable for embedding in the given d-MPCapplication. (Chapters 2 and 5)

• The Lagrange multiplier µ ensures that flexible loads causing congestion are deleted or shiftedwithin the prediction horizon in order to prevent congestion as long as the constraints on theoperation of the heat pump are not violated and the heat demand is fulfilled. (Chapters 5 and8)

• Congestion can only be detected within the prediction horizon. Flexible loads can only beshifted within the prediction horizon. Consequently, congestion can only be prevented withinthe prediction horizon. (Chapters 5 and 8)

• Preventing congestion results in worse performance with respect to minimising the overallimbalance since the congestion management alters the optimal sequence that minimises theoverall imbalance of the network. (Chapters 5 and 8)

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Besides these main findings relating to congestion management in general and the use of the Lagrangemultiplier µ in specific, several other conclusions can be drawn.

• The given d-MPC application acting as starting point for this thesis is not able to properlyreflect the interest of the BRP since there is an discrepancy between the objective function ofthe d-MPC application and the total physical imbalance of a network of prosumers. (Section6.6)

• The proposed division of the DAP into prosumer specific goal functions based up the quantifi-cation of flexibility is a more natural way than the division used in previous work. (Section 5.3and Chapter 8)

9.1 Discussion

The d-MPC presented in this thesis acts as an algorithm that can be applied in the operate phaseof the complex MCM in USEF, consisting out of multiple operating regimes, operating phases andactive actors. The current application is bounded to the green and yellow regime of the operatephase of USEF. The plan and validate phase of USEF are incorporated by using the output of theseiterative phases, the DAP as input for the d-MPC application in the operate phase (remark 4) ThisDAP is assumed to be static and thereby not up to alteration by the BRP in the operate phaseduring the optimisation as the result of possible changing marking conditions. MPC, however, isable to allow changing the desired trajectory, the DAP, at every time step k in the simulation period(remark 5). In the current application, the algorithm already takes new information regarding theimbalance of prosumers, the characteristics of their flexible device into account. Also the objectivefunction can be different for different prosumers and can differ in time.

In Chapter 7, the following assumptions regarding the topology of the system are made. The d-MPCapplication only considers the role of a single BRP, a single DSO, a single aggregator and a smallamount of a maximum of 20 prosumers in the green and yellow operate regimes within the operatephase of USEF. USEF makes no design choices on the number of BRPs, the number of aggregatorsselling flexibility to a single BRP and the number of prosumers on behalf of which the aggregatoraccumulates the flexibility. By considering only a single BRP the trading market between multipleBRPs is neglected (Pons, 2013). The d-MPC application of Doddema (2014) solely addresses asingle aggregator and for reasons of simplicity and the focus on the DSO this number of aggregatorsis not extended.

Moreover, only a single transformer and associated constraint is simulated, although the additionof an extra transformer constraint is shortly mentioned. An additional Lagrange multiplier and anadditional sub-gradient method in order to find a sequence of control inputs without congestion canbe added to Algorithm 3. The algorithm will iterate until the update of the Lagrange multiplier λis converged to the threshold ε and both Lagrange multipliers associated each with the constrainton a different transformer ensures a sequence of control inputs that does not violate any of theconstraints. In that case there is no distinction in different DSOs safeguarding an individual trans-former since the algorithm would not prioritise one capacity constraint over the other with respectto alternating flexible loads. Moreover, only loads of prosumers connected to a specific transformercould prevent congestion on that same transformer. A complicating factor arises when neighboursthat are connected in the information matrix A and share information are not physical neighboursand thereby do not share the same capacity constraint.

The application of Pons (2013) made a start in exploring the effect of multiple aggregators. In thatcase, a BRP can decide from which aggregators it wants to procure flexibility in order to minimisethe total imbalance of the network. It is the task of the aggregator to maximise the value of flexibilitybrought forward by the prosumers it represents. Since the d-MPC application does not consider real

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market prices, how this must be ensured is up to grasps. With respect to congestion managementthe same analogy holds true. Since the prosumers belonging to a single aggregator do not necessarilyhave to be physical neighbours, any congestion at a specific transformer might be solvable via theflexibility accumulated by any aggregator with prosumers connected to that transformer. The currentapplication would not make any distinction and alters those loads that will ensure the minimisation ofthe performance indicator. In the real life market with real market prices, such a distinction will takeplace. The Lagrange multiplier, or shadow price, is hard to interpret in terms of market prices.

With respect to the maximum number of prosumers used within the simulations, a small number ischosen making it easier to comprehend how the algorithm works and how congestion is prevented.The number of prosumers connected to a single low voltage transformer ranges typically around 200.Besides the complexity of understanding the working of the proposed algorithm and the challenge toillustrate the results, 200 prosumers would cause substantial and impractical computation times. Forexample, running 200 households for 96 time steps of 15 minutes (24 hours) with a prediction horizonof only 6 time steps (1.5 hours) and an average amount of 200 iterations per time step results in23 million systems of 68 equations of 68 variables to be solved, which takes approximately 15 hourswith MATLAB version r2014a Mac OS 64-bit and Gurobi solver version 6.0.0 on my Macbook 20113.3 GHz i7 with 4 GB of RAM. Obviously, in a future real-life setting, each prosumer will optimise itsown objective function in parallel rather then one central computer solving all objective functions insequence. Moreover, MATLAB and Gurobi are just tools used to simulate the algorithm. Differenttools will have to be used in the future real-life setting. An often mentioned thumb of role, asexplained by an employee at DNV GL working on USEF is that calculations necessary per prosumershould consume less than 1 kW and 1 euro in a future real-life setting in order to be applicable.

9.2 Future Research

The transition to smart grids is forced by observable trends and ideas on how such an smart gridshould look like, of which USEF is one idea. The presented d-MPC application as presented here isthe result of approximately 5 years of research, including a PhD and, including this work, 3 Mastertheses and still possess many unanswered questions and shortcomings. Based on the discussion onthis work as presented here before, some future topics of interest can be mentioned.

• Increasing the amount of DSOs (i.e. the amount of transformers) will bring more complexproblems at the table ought to be solved. Especially when informational neighbours are notphysical neighbours but, in the current modelling, do share information including the Lagrangemultiplier µ of a specific transformer to which the prosumers might not be connected.

• The quantification of flexibility and the proposed method of dividing the DAP into prosumerspecific goal functions based upon this quantification provides plenty leads for future research.The presumption that it yields a better performing algorithm by a larger number of prosumersprevails. Due to time constraints in this thesis and the applied focus on the DSO, an analysisfor a larger number of prosumers is omitted and of interest for future research.

• The notion of the DAP and the prosumers individual goal function is not well understood interms of how it mathematically behaves as a desired trajectory of the d-MPC. For instance,in Biegel (2012a), the desired trajectory is directly defined within the objective function ratherthan in the dynamic state equation as it is in the current d-MPC application. In that case theprosumer specific portions of the DAP are not required and a fully distributed MPC algorithmis applicable.

• As Doddema (2014) did to work of Pons (2013), the work presented here needs to be extendedwith respect to scalability on the number of prosumers. The work of Doddema on parallelcomputing is not considered within this thesis.

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• With respect to the work of Pons (2013), the application presented here should be extendedwith multiple aggregators. Pons made a first exploration upon this extension but is left asidewithin this work.

• In order for the BRP to have an active role in the operate phase of USEF, the applicationshould be extended such that the DAP can be altered during the optimisation if changingmarket conditions require the BRP to do so.

• This application solely considers heat pumps as flexible appliances and ignores the energyproducing µ-CHP or even energy storage appliances like electrical vehicles. Including multipledifferent appliances increases the amount of flexibility and thereby also the possibilities onresolving congestion within the operate phase of USEF. Moreover, it will better reflect thefuture’s reality given the current observed trends.

• The application lacks any notion of real prices and purely considers shadow prices as economicsignals as the external trigger in the market mechanism. By having a notion of real prices, thevalue of flexibility can be assessed. Moreover, it allows for a proper understanding of the divisionof this value among the different actors that either sell or procure flexibility. Consequently,business cases can be developed.

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